Skip to main content
SpringerLink
Log in
Book cover

L² Approaches in Several Complex Variables pp 1–40Cite as

Basic Notions and Classical Results

  • Chapter

  • 1564 Accesses

Part of the book series: Springer Monographs in Mathematics ((SMM))

Abstract

As a preliminary, basic properties of holomorphic functions and complex manifolds are recalled. Beginning with the definitions and characterizations of holomorphic functions, we shall give an overview of the classical theorems in several complex variables, restricting ourselves to extremely important ones for the discussion in later chapters. Most of the materials presented here are contained in well-written textbooks such as Gunning and Rossi (Analytic functions of several complex variables. Prentice-Hall, Englewood Cliffs, xiv+317 pp, 1965), Hörmander (An introduction to complex analysis in several variables. North-Holland Mathematical Library, vol 7, 3rd edn. North-Holland, Amsterdam, xii+254 pp, 1990), Wells and Raymond (Differential analysis on complex manifolds, Third edition. With a new appendix by Oscar Garcia-Prada. Graduate Texts in Mathematics, vol 65. Springer, New York, 2008), Grauert and Remmert (Theory of Stein spaces, Translated from the German by Alan Huckleberry. Reprint of the 1979 translation. Classics in mathematics. Springer, Berlin, xxii+255 pp, 2004), Grauert and Remmert (Coherent analytic sheaves, Grundlehren der Mathematischen Wissenschaften, vol 265. Springer, Berlin, xviii+249 pp, 1984) and Noguchi (Analytic function theory of several variables —Elements of Oka’s coherence, preprint (translated from Japanese)) (see also Demailly, Analytic methods in algebraic geometry. Surveys of modern mathematics, vol 1. International Press, Somerville; Higher Education Press, Beijing, viii+231 pp, 2012 and Ohsawa, Analysis of several complex variables. Translated from the Japanese by Shu Gilbert Nakamura. Translations of mathematical monographs. Iwanami series in modern mathematics, vol 211. American Mathematical Society, Providence, xviii+121 pp, 2002), so that only sketchy accounts are given for most of the proofs and historical backgrounds. An exception is Serre’s duality theorem. It will be presented after an article of Laurent-Thiébaut and Leiterer (Nagoya Math J 154:141–156, 1999), since none of the above books contains its proof in full generality.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   89.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Bibliography

  1. Adachi, M., Brinkschulte, J.: Curvature restrictions for Levi-flat real hypersurfaces in complex projective planes, to appear in Ann. de l’Inst. Fourier

    Google Scholar 

  2. Ahlfors, L.V.: Conformal Invariants, Topics in Geometric Function Theory, xii+162 pp. Reprint of the 1973 original. With a foreword by Peter Duren, F. W. Gehring and Brad Osgood. AMS Chelsea Publishing, Providence (2010)

    Google Scholar 

  3. Ahlfors, L.V., Beurling, A.: Conformal invariants and function-theoretic null-sets. Acta Math. 33, 105–129 (1950)

    MathSciNet  MATH  Google Scholar 

  4. Akizuki, Y., Nakano, S.: Note on Kodaira-Spencer’s proof of Lefschetz theorems. Proc. Jpn. Acad. 30, 266–272 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  5. Andreotti, A., Gherardelli, F.: Some remarks on quasi-abelian manifolds. In: Global Analysis and Its Applications, vol. II, pp. 203–206. International Atomic Energy Agency, Vienna (1974)

    Google Scholar 

  6. Andreotti, A., Grauert, H.: Théorème de finitude pour la cohomologie des espaces complexes. Bull. Soc. Math. Fr. 90, 193–259 (1962)

    MathSciNet  MATH  Google Scholar 

  7. Andreotti, A., Vesentini, E.: Sopra un teorema di Kodaira. Ann. Scuola Norm. Sup. Pisa 15, 283–309 (1961)

    MathSciNet  MATH  Google Scholar 

  8. Andreotti, A., Vesentini, E.: Carleman estimates for the Laplace-Beltrami equation on complex manifolds. Inst. Hautes Études Sci. Publ. Math. 25, 81–130 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  9. Angehrn, U., Siu, Y.-T.: Effective freeness and point separation for adjoint bundles. Invent. Math. 122, 291–308 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Aronszajn, N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. 36, 235–249 (1957)

    MathSciNet  MATH  Google Scholar 

  11. Barlet, D.: Espace analytique réduit des cycles analytiques complexes compacts d’un espace analytique complexe de dimension finie. In: Fonctions de plusieurs variables complexes, II (Sém. Franois Norguet, 1974–1975). Lecture Notes in Mathematics, vol. 482, pp. 1–158. Springer, Berlin (1975)

    Google Scholar 

  12. Barlet, D.: Convexité de l’espace des cycles. Bull. Soc. Math. Fr. 106, 373–397 (1978)

    MathSciNet  MATH  Google Scholar 

  13. Battaglia, E., Biagi, S., Bonfiglioli, A.: The strong maximum principle and the Harnack inequality for a class of hypoelliptic non-Hörmander operators, preprint

    Google Scholar 

  14. Bayer, D.: The division algorithm and the Hilbert scheme. Ph.D. thesis, Harvard University (1982)

    Google Scholar 

  15. Bedford, E., Taylor, B.A.: Variational properties of the complex Monge-Ampère equation I. Dirichlet principle. Duke Math. J. 45, 375–403 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  16. Bedford, E., Taylor, B.A.: Variational properties of the complex Monge-Ampère equation II. Intrinsic norms. Am. J. Math. 101, 1131–1166 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  17. Behnke, H., Stein, K.: Entwicklung analytischer Funktionen auf Riemannschen Flächen. Math. Ann. 120, 430–461 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  18. Behnke, H., Thullen, P.: Theorie der Funktionen mehrerer komplexer Veränderlichen, Ergebnisse der Mathematik und ihrer Grenzgebiete. (2. Folge) (by Heinrich Behnke, P. Thullen, R. Remmert, W. Barth, O. Forster, W. Kaup, H. Kerner, H. Holmann, H.J. Reiffen, G. Scheja, K. Spallek) Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge (Book 51) Springer, 1970. (Softcover reprint: October 20, 2011)

    Google Scholar 

  19. Behrens, M.: Plurisubharmonic defining functions of weakly pseudoconvex domains in \(\mathbb{C}^{2}\). Math. Ann. 270, 285–296 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  20. Berenstein, C.A., Gay, R., Vidras, A., Yger, A.: Residue Currents and Bezout Identities. Progress in Mathematics, vol. 114, xii+158 pp. Birkhäuser Verlag, Basel (1993)

    Google Scholar 

  21. Bergman, S.: Über die entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthogonalfunktionen. Math. Ann. 86, 238–271 (1922)

    Article  MathSciNet  MATH  Google Scholar 

  22. Berman, R., Berndtsson, B., Sjöstrand, J.: A direct approach to Bergman kernel asymptotics for positive line bundles. Ark. Mat. 46, 197–217 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Berndtsson, B.: Curvature of vector bundles associated to holomorphic fibrations. Ann. Math. 169, 531–560 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  24. Berndtsson, B.: The openness conjecture for plurisubharmonic functions. arXiv: 1305.5781

    Google Scholar 

  25. Berndtsson, B., Lempert, L.: A proof of the Ohsawa-Takegoshi theorem with sharp estimates, arXiv: 140/.4946v1 [math.CV], 18 July 2014, to appear in J. Math. Soc. Jpn.

    Google Scholar 

  26. Berndtsson, B., Păun, M.: Bergman kernels and the pseudoeffectivity of relative canonical bundles. Duke Math. J. 145, 341–378 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  27. Bierstone, E., Milman, P.; Relations among analytic functions I. Ann. Inst. Fourier 37, 187–239 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  28. Bierstone, E., Milman, P.: Uniformization of analytic spaces. J. Am. Math. Soc. 2, 801–836 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  29. Birkenhake, C., Lange, H.: Complex Abelian Varieties. Grundlehren der Mathematischen Wissenschaften, vol. 302, 2nd edn., xii+635 pp. Springer, Berlin (2004)

    Google Scholar 

  30. Bishop, E.: Mappings of partially analytic spaces. Am. J. Math. 83, 209–242 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  31. Błocki, Z.: The Bergman metric and the pluricomplex Green function. Trans. Am. Math. Soc. 357, 2613–2625 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  32. Błocki, Z.: Suita conjecture and the Ohsawa-Takegoshi extension theorem. Invent. Math. 193, 149–158 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  33. Błocki, Z.: A lower bound for the Bergman kernel and the Bourgain-Milman inequality. In: Klartag, B., Milman, E. (eds.) Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 2011–2013. Lecture Notes in Mathematics, vol. 2116, pp. 53–63. Springer (2014)

    Google Scholar 

  34. Błocki, Z., Pflug, P.: Hyperconvexity and Bergman completeness. Nagoya Math. J. 151, 221–225 (1998)

    MathSciNet  MATH  Google Scholar 

  35. Bochner, S.: Über orthogonale Systeme analytischer Funktionen. Math. Z. 14, 180–207 (1922)

    Article  MathSciNet  MATH  Google Scholar 

  36. Bombieri, E.: Algebraic values of meromorphic maps. Invent. Math. 10, 267–287 (1970). Addendum: Invent. Math. 11, 163–166 (1970)

    Google Scholar 

  37. Bombieri, E.: The pluricanonical map of a complex surface. In: Several Complex Variables, I. Proceedings of the Conference on University of Maryland, College Park, 1970, pp. 35–87. Springer, Berlin (1970)

    Google Scholar 

  38. Boucksom, S., Favre, C., Jonsson, M.: Valuations and plurisubharmonic singularities. Publ. RIMS 44, 449–494 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  39. Bouligand, G.: Sur les problème de Dirichlet. Ann. Soc. Polonaise de Math. 4, 59–112 (1925)

    MATH  Google Scholar 

  40. Bremermann, H.J.: On the conjecture of the equivalence of the plurisubharmonic functions and the Hartogs functions. Math. Ann. 131, 76–86 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  41. Briancon, J., Skoda, H.: Sur la clôture intégrale d’un idéal de germes de fonctions holomorphes en un point de \(\mathbb{C}^{n}\). C. R. Acad. Sci. Paris Sér. A 278, 949–951 (1974)

    MathSciNet  MATH  Google Scholar 

  42. Brunella, M.: A positivity property for foliations on compact Kähler manifolds. Int. J. Math. 17, 35–43 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  43. Brunella, M.: On the dynamics of codimension one holomorphic foliations with ample normal bundle. Indiana Univ. Math. J. 57, 3101–3113 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  44. Brunella, M.: Codimension one foliations on complex tori. Ann. Fac. Sci. Toulouse Math. 19, 405–418 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. Brunella, M.: Birational Geometry of Foliations. IMPA Monographs, vol. 1, 124 p. Springer, Cham (2015)

    Google Scholar 

  46. Camacho, C., Lins Neto, A., Sad, P.: Minimal sets of foliations on complex projective spaces. Inst. Hautes Études Sci. Publ. Math. 68, 187–203 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  47. Cao, J.-Y.: Numerical dimension and a Kawamata-Viehweg-Nadel-type vanishing theorems on compact Kähler manifolds. Compos. Math. 150, 1869–1902 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  48. Cao, J.-Y.: Ohsawa-Takegoshi extension theorem for compact Kähler manifolds and applications. arXiv: 1404.6937

    Google Scholar 

  49. Cao, J., Shaw, M.-C.: The \(\bar{\partial }\)-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in \(\mathbb{C}\mathbb{P}^{n}\) with n ≥ 3. Math. Z. 256, 175–192 (2007)

    Google Scholar 

  50. Capocasa, F., Catanese, F.: Periodic meromorphic functions. Acta Math. 166, 27–68 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  51. Carleson, L.: Selected Problems on Exceptional Sets. Van Nostrand Mathematical Studies, No. 13, v+151 pp. D. Van Nostrand, Princeton/Toronto/London (1967)

    Google Scholar 

  52. Cartan, H.: Idéaux et modules de fonctions analytiques de variables complexes. Bull. Soc. Math. Fr. 78, 29–64 (1950)

    MathSciNet  MATH  Google Scholar 

  53. Cartan, H., Thullen, P.: Zur Theorie der Singularitäten der Funktionen mehrerer komplexen Veränderlichen: Regularitäts–  und Konvergenz–bereiche. Math Ann. 106, 617–647 (1932)

    Google Scholar 

  54. Catlin, D.: The Bergman kernel and a theorem of Tian. In: Analysis and Geometry in Several Complex Variables, Katata, 1997. Trends in Mathematics, pp. 1–23. Birkhäuser, Boston (1999)

    Google Scholar 

  55. Cerveau, D.: Minimaux des feuilletages algébriques de \(\mathbb{C}\mathbb{P}^{n}\). Ann. Inst. Fourier (Grenoble) 43, 1535–1543 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  56. Cerveau, D., Lins Neto, A.: A structural theorem for codimension-one foliations on \(\mathbb{P}^{n}\), n ≥ 3, with an application to degree-three foliations. Ann. Sc. Norm. Super. Pisa 12, 1–41 (2013)

    Google Scholar 

  57. Cheeger, J., Goresky, M., MacPherson, R.: L 2-cohomology and intersection homology of singular algebraic varieties. In: Yau, S.-T. (ed.) Seminar on Differential Geometry, pp. 303–340. Princeton University Press, Princeton (1982)

    Google Scholar 

  58. Chen, B.-Y.: Bergman completeness of hyperconvex manifolds. Nagoya Math. J. 175, 165–170 (2004)

    MathSciNet  MATH  Google Scholar 

  59. Chen, B.-Y.: A simple proof of the Ohsawa-Takegoshi extension theorem. arXiv:math.CV/. 1105.2430

    Google Scholar 

  60. Chow, W.-L., Kodaira, K.: On analytic surfaces with two independent meromorphic functions. Proc. Natl. Acad. Sci. U.S.A. 38, 319–325 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  61. Chow, W.-L.: On compact complex analytic varieties. Am. J. Math. 71, 893–914 (1949)

    Article  MATH  MathSciNet  Google Scholar 

  62. Coeuré, G., Loeb, J.J.: A counterexample to the Serre problem with a bounded domain of \(\mathbb{C}^{2}\) as fiber. Ann. Math. 122, 329–334 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  63. de Cataldo, M.A.A.: Singular Hermitian metrics on vector bundles. J. Reine Angew. Math. 502, 93–122 (1998)

    MathSciNet  MATH  Google Scholar 

  64. Demailly, J.-P.: Un example de fibré holomorphe non de Stein à fibre \(\mathbb{C}^{2}\) ayant pour base le disque ou le plan. Invent. Math. 48, 293–302 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  65. Demailly, J.-P.: Estimations L 2 pour l’opérateur \(\bar{\partial }\) d’un fibré vectoriel holomorphe semi-positif au-dessus d’une variété kählérienne complète. Ann. Sci. École Norm. Sup. 15, 457–511 (1982)

    MathSciNet  MATH  Google Scholar 

  66. Demailly, J.-P.: Sur l’identité de Bochner-Kodaira-Nakano en géométrie hermitienne. Lecture Notes in Mathematics, vol. 1198, pp. 88–97. Springer, Berlin/Heidelberg (1985)

    Google Scholar 

  67. Demailly, J.-P.: Une généralisation du théorème d’annulation de Kawamata-Viehweg. C. R. Acad. Sci. Paris Sér. I Math. 309, 123–126 (1989)

    MathSciNet  MATH  Google Scholar 

  68. Demailly, J.-P.: Cohomology of q-convex spaces in top degrees. Math. Z. 204, 283–295 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  69. Demailly, J.-P.: Regularization of closed positive currents and intersection theory. J. Algebr. Geom. 1, 361–409 (1992)

    MathSciNet  MATH  Google Scholar 

  70. Demailly, J.-P.: On the Ohsawa-Takegoshi-Manivel L 2 extension theorem. In: Complex Analysis and Geometry. Progress in Mathematics, vol. 188, pp. 47–82. Birkhäuser, Basel/Boston (2000)

    Google Scholar 

  71. Demailly, J.-P.: Multiplier ideal sheaves and analytic methods in algebraic geometry. In: School on Vanishing Theorems and Effective Results in Algebraic Geometry (Trieste, 2000). ICTP Lecture Notes, vol. 6, pp. 1–148. Abdus Salam International Centre for Theoretical Physics, Trieste (2001)

    Google Scholar 

  72. Demailly, J.-P.: Analytic Methods in Algebraic Geometry. Surveys of Modern Mathematics, vol. 1, viii+231 pp. International Press/Higher Education Press, Somerville/Beijing (2012)

    Google Scholar 

  73. Demailly, J.-P., Ein, L., Lazarsfeld, R: A subadditivity property of multiplier ideals. Dedicated to William Fulton on the occasion of his 60th birthday. Mich. Math. J. 48, 137–156 (2000)

    Google Scholar 

  74. Demailly, J.-P., Kollár, J.: Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds. Ann. Sci. École Norm. Sup. 34, 525–556 (2001)

    MATH  Google Scholar 

  75. Demailly, J.-P., Peternell, T.: A Kawamata-Viehweg vanishing theorem on compact Kähler manifolds. J. Differ. Geom. 63, 231–277 (2003)

    MathSciNet  MATH  Google Scholar 

  76. Demailly, J.-P., Peternell, T., Schneider, M.: Pseudo-effective line bundles on compact Kähler manifolds. Int. J. Math. 12, 689–741 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  77. Demailly, J.-P., Skoda, H.: Relations entre les notions de positivité de P.A. Griffiths et de S. Nakano, Seminaire P. Lelong-H. Skoda (Analyse), année 1978/79. Lecture Notes in Mathematics, vol. 822, pp. 304–309. Springer, Berlin (1980)

    Google Scholar 

  78. Diederich, K.: Das Randverhalten der Bergmanschen Kernfunktion und Metrik in streng pseudo-konvexen Gebieten. Math. Ann. 187, 9–36 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  79. Diederich, K., Fornaess, J.E.: Pseudoconvex domains: bounded strictly plurisubharmonic exhaustion functions. Invent. Math. 39, 129–141 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  80. Diederich, K., Fornaess, J.E.: Smooth, but not complex-analytic pluripolar sets. Manuscr. Math. 37, 121–125 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  81. Diederich, K., Fornaess, J.E.: A smooth curve in \(\mathbb{C}^{2}\) which is not a pluripolar set. Duke Math. J. 49, 931–936 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  82. Diederich, K., Fornaess, J.E.: Thin complements of complete Kähler domains. Math. Ann. 259, 331–341 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  83. Diederich, K., Fornaess, J.E.: A smooth pseudoconvex domain without pseudoconvex exhaustion. Manuscr. Math. 39, 119–123 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  84. Diederich, K., Fornaess, J.E.: On the nature of thin complements of complete Kähler metrics. Math. Ann. 268, 475–495 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  85. Diederich, K., Ohsawa, T.: A Levi problem on two-dimensional complex manifolds. Math. Ann. 261, 255–261 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  86. Diederich, K., Ohsawa, T.: Harmonic mappings and disc bundles over compact Kähler manifolds. Publ. Res. Inst. Math. Sci. 21, 819–833 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  87. Diederich, K., Ohsawa, T.: On the parameter dependence of solutions to the \(\bar{\partial }\)-equation. Math. Ann. 289, 581–587 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  88. Diederich, K., Ohsawa, T.: An estimate for the Bergman distance on pseudoconvex domains. Ann. Math. 141, 181–190 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  89. Diederich, K., Pflug, P.: Über Gebiete mit vollständiger Kählermetrik. Math. Ann. 257, 191–198 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  90. Donaldson, S.K.: Scalar curvature and projective embeddings I. J. Differ. Geom. 59, 479–522 (2001)

    MathSciNet  MATH  Google Scholar 

  91. Donnelly, H., Fefferman, C.: L 2-cohomology and index theorem for the Bergman metric. Ann. Math. 118, 593–618 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  92. Ein, L., Lazarsfeld, R.: Global generation of pluricanonical and adjoint linear series on smooth projective threefolds. J. Am. Math. Soc. 6, 875–903 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  93. Eisenbud, D.: Commutative Algebra with a View Toward Algebraic Geometry. Graduate Texts in Mathematics, vol. 150. Springer, New York (1995)

    Google Scholar 

  94. Eisenbud, D., Evans, E.G., Jr.: Every algebraic set in n-space is the intersection of n hypersurfaces. Invent. Math. 19, 107–112 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  95. Elencwajg, G.: Pseudo-convexité locale dans les variétés kählériennes. Ann. Inst. Fourier (Grenoble) 25, 295–314 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  96. Eliashberg, Y., Gromov, M.: Embeddings of Stein manifolds of dimension n into the affine space of dimension 3n/2+1. Ann. Math. 136, 123–135 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  97. Eyssidieux, P., Katzarkov, L., Pantev, T., Ramachandran, M.: Linear Shafarevich conjecture. Ann. Math. 176, 1545–1581 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  98. Favre, C., Jonsson, M.: Valuations and multiplier ideals. J. Am. Math. Soc. 18, 655–684 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  99. Fefferman, C.: Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains. Ann. Math. 103, 395–416 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  100. Fujiki, A.: On the blowing down of analytic spaces. Publ. Res. Inst. Math. Sci. 10, 473–507 (1974/1975)

    Google Scholar 

  101. Fujiki, A.: An L 2 Dolbeault lemma and its applications. Publ. Res. Inst. Math. Sci. 28, 845–884 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  102. Fujiki, A., Nakano, S.: Supplement to “On the inverse of monoidal transformation”. Publ. Res. Inst. Math. Sci. 7, 637–644 (1971/1972)

    Google Scholar 

  103. Fujita, R.: Domaines sans point critique intérieur sur l’espace projectif complexe. J. Math. Soc. Jpn. 15, 443–473 (1963)

    Article  MATH  Google Scholar 

  104. Fujita, T.: On Kähler fiber spaces over curves. J. Math. Soc. Jpn. 30, 779–794 (1978)

    Article  MATH  Google Scholar 

  105. Fujita, T.: On polarized manifolds whose adjoint bundles are not semipositive. In: Algebraic Geometry, Sendai, 1985. Advanced Studies in Pure Mathematics, vol. 10, pp. 167–178 (1987)

    Google Scholar 

  106. Fujita, T.: Remarks on Ein-Lazarsfeld criterion of spannedness of adjoint bundles of polarized threefolds, preprint 1993

    Google Scholar 

  107. Gaffney, M.P.: A special Stokes’s theorem for complete Riemannian manifolds. Ann. Math. 60, 140–145 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  108. Galligo, A.: Théorème de division et stabilité en géométrie analytique locale. Ann. Inst. Fourier 29, 107–184 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  109. Ghys, É.: Feuilletages holomorphes de codimension un sur les espaces homogènes complexes. Ann. Fac. Sci. Toulouse Math. 5, 493–519 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  110. Gong, X.-H., Kim, K.-T.: The \(\bar{\partial }\)-equation on variable strictly pseudoconvex domains. Preprint

    Google Scholar 

  111. Grauert, H.: Charakterisierung der holomorph vollständigen komplexen Räume. Math. Ann. 129, 233–259 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  112. Grauert, H.: Charakterisierung der Holomorphiegebiete durch die vollständige Kählersche Metrik. Math. Ann. 131, 38–75 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  113. Grauert, H.: On Levi’s problem and the imbedding of real-analytic manifolds. Ann. Math. 68, 460–472 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  114. Grauert, H.: Ein Theorem der analytischen Garbentheorie und die Modulräume komplexer Strulturen. Inst. H. E. S. Publ. Math. 233–292 (1960)

    Google Scholar 

  115. Grauert, H.: Über Modifikationen und exzeptionelle analytische Mengen. Math. Ann. 146, 331–368 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  116. Grauert, H.: Bemerkenswerte pseudokonvexe Mannigfaltigkeiten. Math. Z. 81, 377–391 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  117. Grauert, H., Remmert, R.: Theory of Stein Spaces (Translated from the German by Alan Huckleberry). Reprint of the 1979 translation. Classics in Mathematics, xxii+255 pp. Springer, Berlin (2004)

    Google Scholar 

  118. Grauert, H., Remmert, R.: Coherent Analytic Sheaves. Grundlehren der Mathematischen Wissenschaften, vol. 265, xviii+249 pp. Springer, Berlin (1984)

    Google Scholar 

  119. Grauert, H., Riemenschneider, O.: Kählersche Mannigfaltigkeiten mit hyper-q-konvexem Rand. In: Problems in Analysis. Lectures Symposium in Honor of Salomon Bochner. Princeton University, Princeton, 1969, pp. 61–79. Princeton University Press, Princeton (1970)

    Google Scholar 

  120. Grauert, H., Riemenschneider, O.: Verschwindungssätze für analytische Kohomologiegruppen auf komplexen Räumen. Invent. Math. 11, 263–292 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  121. Greene, R.E., Wu, H.-H.: Embedding of open Riemannian manifolds by harmonic functions. Ann. Inst. Fourier 25, 215–235 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  122. Greene, R.E., Wu, H.-H.: Integrals of subharmonic functions on manifolds of nonnegative curvature. Invent. Math. 27, 265–298 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  123. Greene, R.E., Wu, H.-H.: Some function-theoretic properties of noncompact Kähler manifolds. In: Differential Geometry. Proceedings of Symposia in Pure Mathematics, vol. XXVII, Part 2, Stanford University, Stanford, 1973, pp. 33–41. American Mathematical Society, Providence (1975)

    Google Scholar 

  124. Greene, R.E., Wu, H.-H.: Gap theorems for noncompact Riemannian manifolds. Duke Math. J. 49, 731–756 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  125. Griffiths, P.A.: Periods of integrals on algebraic manifolds. I and II. Am. J. Math. 90, 568–626 and 805–865 (1968)

    Google Scholar 

  126. Griffiths, P.A.: Hermitian differential geometry, Chern classes, and positive vector bundles. In: Global Analysis. Papers in Honor of K. Kodaira, pp. 185–251. University Tokyo Press, Tokyo (1969)

    Google Scholar 

  127. Griffiths, Ph.A.: Periods of integrals on algebraic manifolds. III, some global differential-geometric properties of the period mapping. Inst. Hautes Études Sci. Publ. Math. 38, 125–180 (1970)

    Google Scholar 

  128. Gromov, M.: Kähler hyperbolicity and L 2-Hodge theory. J. Differ. Geom. 33, 263–292 (1991)

    MathSciNet  MATH  Google Scholar 

  129. Greene, R.E., Krantz, S.G.: The stability of the Bergman kernel and the geometry of the Bergman metric. Bull. Am. Math. Soc. 4, 111–115 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  130. Grothendieck, A.: La théorie des classes de Chern. Bull. Soc. Math. Fr. 86, 137–154 (1958)

    MathSciNet  MATH  Google Scholar 

  131. Grothendieck, A.: Sur une note de Mattuck-Tate. J. Reine Angew. Math. 200, 208–215 (1958)

    MathSciNet  MATH  Google Scholar 

  132. Guan, Q.-A., Zhou, X.-Y.: A solution of an L2 extension problem with optimal estimate and applications. Ann. Math. 181, 1139–1208 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  133. Guan, Q.-A., Zhou, X.-Y.: Strong openness conjecture for plurisubharmonic functions (2013). arXiv:1311.3/81v1

    Google Scholar 

  134. Guan, Q.-A., Zhou, X.-Y.: Strong openness conjecture and related problems for plurisubharmonic functions (2014). arXiv:1401.7158v1

    Google Scholar 

  135. Guan, Q.-A., Zhou, X.-Y.: Classification of multiplier ideal sheaf with Lelong number one weight (2014). arXiv:1411.6737v1

    Google Scholar 

  136. Guan, Q.-A., Zhou, X.-Y.: A proof of Demailly’s strong openness conjecture, preprint

    Google Scholar 

  137. Gunning, R.C., Rossi, H.: Analytic Functions of Several Complex Variables, xiv+317 pp. Prentice-Hall, Englewood Cliffs (1965)

    Google Scholar 

  138. Hamano, S.: Variation formulas for L 1-principal functions and application to the simultaneous uniformization problem. Mich. Math. J. 60, 271–288 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  139. Hartogs, F.: Zur Theorie der analytischen Funktionen mehrerer unabhängiger Veränderlichen insbesondere über die Darstellung derselben durch Reihen, welche nach Potenzen einer Veränderlichen fortschreiten. Math. Ann. 62, 1–88 (1906)

    Article  MathSciNet  MATH  Google Scholar 

  140. Heier, G.: Effective freeness of adjoint line bundles. Doc. Math. 7, 31–42 (2002)

    MathSciNet  MATH  Google Scholar 

  141. Helmke, S.: On Fujita’s conjecture. Duke Math. J. 88, 201–216 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  142. Helmke, S.: On global generation of adjoint linear systems. Math. Ann. 313, 635–652 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  143. Henkin, G.M.: The method of integral representations in complex analysis. In: Several Complex Variables I. Encyclopaedia of Mathematical Sciences, vol. 7, pp. 19–116. Springer, Berlin/New York (1990). (The English translation of the article in) Current problems in mathematics. Fundamental directions, vol. 7, 23–124, 258, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow (1985)

    Google Scholar 

  144. Herbort, G.: The Bergman metric on hyperconvex domains. Math. Z. 232, 183–196 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  145. Hiep, P.H.: The weighted log canonical threshold (2014). arXiv:1401.4833v5

    Google Scholar 

  146. Hironaka, H.: Flattening theorem in complex-analytic geometry. Am. J. Math. 97, 503–547 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  147. Hironaka, H., Urabe, T.: Kaiseki kukan nyumon. (Japanese) (Introduction to analytic spaces), 2nd edn. Suri Kagaku Raiburari (Mathematical Science Library), 1, vi+158 pp. Asakura Publishing Co., Tokyo (1983)

    Google Scholar 

  148. Hirschowitz, A.: Pseudoconvexité au-dessus d’espaces plus ou moins homogènes. Invent. Math. 26, 303–322 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  149. Hodge, W.V.D.: The Theory and Applications of Harmonic Integrals. Cambridge University Press, Cambridge (1941)

    MATH  Google Scholar 

  150. Hopf, H.: Zur Topologie der komplexen Mannigfaltigkeiten. Studies and Essays Presented to R. Courant on his 60th Birthday, January 8, 1948, pp. 167–185. Interscience Publishers, New York (1948)

    Google Scholar 

  151. Hörmander, L.: L 2 estimates and existence theorems for the \(\bar{\partial }\) operator. Acta Math. 113, 89–152 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  152. Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North-Holland Mathematical Library, vol. 7, 3rd edn, xii+254 pp. North-Holland Publishing, Amsterdam (1990)

    Google Scholar 

  153. Hörmander, L.: A history of existence theorems for the Cauchy-Riemann complex in L 2 spaces. J. Geom. Anal. 13, 329–357 (2003)

    Article  MathSciNet  Google Scholar 

  154. Hörmander, L., Wermer, J.: Uniform approximation on compact sets in \(\mathbb{C}^{n}\). Math. Scand. 23, 5–21 (1968)

    MathSciNet  MATH  Google Scholar 

  155. Hsiang, W.C., Pati, V.: L 2-cohomology of normal algebraic surfaces. I. Invent. Math. 81, 395–412 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  156. Huber, A.: On subharmonic functions and differential geometry in the large. Comment. Math. Helv. 32, 13–72 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  157. Huckleberry, A.: On certain domains in cycle spaces of flag manifolds. Math. Ann. 323, 797–810 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  158. Jonsson, M., Mustatá, M.: An algebraic approach to the openness conjecture of Demailly and Kollár. J. Inst. Math. Jussieu 13, 119–144 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  159. Kai, C., Ohsawa, T.: A note on the Bergman metric of bounded homogeneous domains. Nagoya Math. J. 186, 157–163 (2007)

    MathSciNet  MATH  Google Scholar 

  160. Kato, Ma.: Topology of Hopf surfaces. J. Math. Soc. Jpn. 27, 222–238 (1975). Erratum, J. Math. Soc. Jpn. 41, 173–174 (1989)

    Google Scholar 

  161. Kato, Mi.: Some problems in topology. In: Hattori, A. (ed.) Manifolds-Tokyo 1973, Proceedings of the International Conference on Manifolds and Related Topics in Topology Tokyo, 1973, pp. 421–431. University of Tokyo Press, Tokyo (1975)

    Google Scholar 

  162. Kawai, T., Kashiwara, M.: The Poincaré lemma for variations of polarized Hodge structure. Publ. Res. Inst. Math. Sci. 23, 345–407 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  163. Kazama, H.: Approximation theorem and application to Nakano’s vanishing theorem for weakly 1-complete manifolds. Mem. Fac. Sci. Kyushu Univ. 27, 221–240 (1973)

    MathSciNet  MATH  Google Scholar 

  164. Kazama, H.: \(\bar{\partial }\)-cohomology of (H,C)-groups. Publ. Res. Inst. Math. Sci. 20, 297–317 (1984)

    Google Scholar 

  165. Kazama, H.: On pseudoconvexity of complex Lie groups. Mem. Fac. Sci. Kyushu Univ. 27, 241–247 (1973)

    MathSciNet  MATH  Google Scholar 

  166. Kawamata, Y.: A generalization of Kodaira-Ramanujam’s vanishing theorem. Math. Ann. 261, 43–46 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  167. Kawamata, Y.: The cone of curves of algebraic varieties. Ann. Math. 119, 603–633 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  168. Kawamata, Y.: Pluricanonical systems on minimal algebraic varieties. Invent. Math. 79, 567–588 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  169. Kawamata, Y.: On Fujita’s freeness conjecture for 3-folds and 4-folds. Math. Ann. 308, 491–505 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  170. Kawamata, Y.: Higher Dimensional Algebraic Varieties. (Japanese) Iwanami, Tokyo (2014)

    Google Scholar 

  171. Kawamata, Y., Matsuda, K., Matsuki, K.: Introduction to the Minimal Model Problem. Algebraic Geometry, Sendai, 1985. Advanced Studies in Pure Mathematics, vol. 10, pp. 283–360. North-Holland, Amsterdam (1987)

    Google Scholar 

  172. Kempf, G.R.: Complex Abelian Varieties and Theta Functions. Universitext, x+105 pp. Springer, Berlin (1991)

    Google Scholar 

  173. Kerzman, N.: The Bergman kernel function. Differentiability at the boundary. Math. Ann. 195, 149–158 (1972)

    MathSciNet  Google Scholar 

  174. Kerzman, N., Rosay, J.-P.: Fonctions plurisousharmoniques d’exhaustion bornées et domaines taut. Math. Ann. 257, 171–184 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  175. Kim, K.T., Levenberg, N., Yamaguchi, H.: Robin Functions for Complex Manifolds and Applications. Memoirs of the American Mathematical Society, vol. 209, No. 984. American Mathematical Society, Providence (2011)

    Google Scholar 

  176. Kobayashi, S.: Geometry of bounded domains. Trans. Am. Math. Soc. 92, 267–290 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  177. Kobayashi, S.: Differential Geometry of Complex Vector Bundles. Publications of the Mathematical Society of Japan, vol. 15, xii+305 pp. Kanô Memorial Lectures 5. Princeton University Press/Iwanami Shoten, Princeton/Tokyo (1987)

    Google Scholar 

  178. Kodaira, K.: Harmonic fields in Riemannian manifolds (generalized potential theory). Ann. Math. 50, 587–665 (1949)

    Article  MathSciNet  MATH  Google Scholar 

  179. Kodaira, K.: On a differential-geometric method in the theory of analytic stacks. Proc. Natl. Acad. Sci. U.S.A. 39, 1268–1273 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  180. Kodaira, K.: On Kähler varieties of restricted type (an intrinsic characterization of algebraic varieties). Ann. Math. 60, 28–48 (1954)

    Article  MathSciNet  MATH  Google Scholar 

  181. Kodaira, K.: On the structure of compact complex analytic surfaces, II, III. Am. J. Math. 88, 682–721 (1966); 90, 55–83 (1968)

    Google Scholar 

  182. Kohn, J.: Sufficient conditions for subellipticity on weakly pseudo-convex domains. Proc. Natl. Acad. Sci. U.S.A. 74, 2214–2216 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  183. Kohn, J.J., Nirenberg, L.: A pseudo-convex domain not admitting a holomorphic support function. Math. Ann. 201, 265–268 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  184. Kollár, J.: Effective base point freeness. Math. Ann. 296, 595–605 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  185. Krushkal’, S.L.: Strengthening pseudoconvexity of finite-dimensional Teichmüller spaces. Math. Ann. 290, 681–687 (1991)

    Google Scholar 

  186. Lattes, M.S.: Sur les formes réduits des transformations ponctuelles à deux variables. C. R. Acad. Sci. 152, 1566–1569 (1911)

    MATH  Google Scholar 

  187. Laurent-Thiébaut, C., Leiterer, J.: Some applications of Serre duality in CR manifolds. Nagoya Math. J. 154, 141–156 (1999)

    MathSciNet  MATH  Google Scholar 

  188. Levenberg, N., Yamaguchi, H.: The Metric Induced by the Robin Function. Memoirs of the American Mathematical Society, vol. 92, 448, viii+156 pp. American Mathematical Society, Providence (1991)

    Google Scholar 

  189. Levenberg, N., Yamaguchi, H.: Pseudoconvex domains in the Hopf surface. J. Math. Soc. Jpn. 67, 231–273 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  190. Lieb, I., Michel, J.: The Cauchy-Riemann Complex. Integral Formulae and Neumann Problem. Aspects of Mathematics, E34, x+362 pp. Friedr. Vieweg & Sohn, Braunschweig (2002)

    Google Scholar 

  191. Lins Neto, A.: A note on projective Levi flats and minimal sets of algebraic foliations. Ann. Inst. Fourier 49, 1369–1385 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  192. Lipman, J., Tessier, B.: Pseudo-rational local rings and a theorem of Briançon-Skoda. Mich. Math. J. 28, 97–115 (1981)

    Article  MATH  Google Scholar 

  193. Liu, K., Sun, X., Yang, X.: Positivity and vanishing theorems for ample vector bundles. J. Algebr. Geom. 22, 303–331 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  194. Liu, K., Yang, X.: Curvatures of direct image sheaves of vector bundles and applications. J. Differ. Geom. 98, 117–145 (2014)

    MATH  MathSciNet  Google Scholar 

  195. Looijenga, E.: L 2-cohomology of locally symmetric varieties. Compositio Math. 67, 3–20 (1988). About integral closures of ideals, Mich. Math. J. 28, 97–115 (1981)

    Google Scholar 

  196. Mabuchi, T.: Asymptotic structures in the geometry of stability and extremal metrics (English summary). In: Handbook of Geometric Analysis. Advanced Lectures in Mathematics (ALM), vol. 7, No. 1, pp. 277–300. International Press, Somerville (2008)

    Google Scholar 

  197. Maitani, F., Yamaguchi, H.: Variation of Bergman metrics on Riemann surfaces. Math. Ann. 330, 477–489 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  198. Matsushima, Y., Morimoto, A.: Sur certains espaces fibrés holomorphes sur une variété de Stein. Bull. Soc. Math. Fr. 88, 137–155 (1960)

    MathSciNet  MATH  Google Scholar 

  199. Matsumoto, K.: Levi form of logarithmic distance to complex submanifolds and its application to developability. In: Complex Analysis in Several Variables – Memorial Conference of Kiyoshi Oka’s Centennial Birthday. Advanced Studies in Pure Mathematics, vol. 42, pp. 203–207. Mathematical Society of Japan, Tokyo (2004)

    Google Scholar 

  200. Merker, J., Porten, E.: The Hartogs extension theorem on (n-1)-complete complex spaces. J. Reine Angew. Math. 637, 23–39 (2009)

    MathSciNet  MATH  Google Scholar 

  201. Miebach, C.: Pseudoconvex non-Stein domains in primary Hopf surfaces. Izv. Math. 78, 1028–1035 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  202. Milnor, J.: On deciding whether a surface is parabolic or hyperbolic. Am. Math. Mon. 84, 43–46 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  203. Mok, N.: The Serre problem on Riemann surfaces. Math. Ann. 258, 145–168 (1981/1982)

    Google Scholar 

  204. Mok, N., Yau, S.-T.: Completeness of the Kähler-Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions. In: The Mathematical Heritage of Henri Poincaré, Part 1, Bloomington, 1980. Proceedings of Symposia in Pure Mathematics, vol. 39, pp. 41–59. American Mathematical Society, Providence (1983)

    Google Scholar 

  205. Mori, S.: Projective manifolds with ample tangent bundles. Ann. Math. 110, 593–606 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  206. Mori, S.: Threefolds whose canonical bundles are not numerically effective. Ann. Math. 116, 133–176 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  207. Morimoto, A.: Non-compact complex Lie groups without non-constant holomorphic functions. In: Proceedings of the Conference on Complex Analysis, Minneapolis 1964, pp. 256–272. Springer (1965)

    Google Scholar 

  208. Morrey, C.B., Jr.: The analytic embedding of abstract real-analytic manifolds. Ann. Math. 68, 159–201 (1958)

    Article  MathSciNet  MATH  Google Scholar 

  209. Mourougane, C., Takayama, S.: Hodge metrics and positivity of direct images. J. für die reine u. angew. Mathematik 606, 167–178 (2007)

    MathSciNet  MATH  Google Scholar 

  210. Mumford, D.: The topology of normal singularities of an algebraic surface and a criterion for simplicity. Inst. Hautes Études Sci. Publ. Math. 9, 5–22 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  211. Nadel, A.: Multiplier ideal sheaves and Kähler-Einstein metrics of positive scalar curvature. Ann. Math. 132, 549–596 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  212. Nagase, M.: Remarks on the L 2-cohomology of singular algebraic surfaces. J. Math. Soc. Jpn. 41, 97–116 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  213. Nagata, M.: Local Rings. Interscience Tracts in Pure and Applied Mathematics, No. 13, xiii+234 pp. Interscience Publishers a division of John Wiley & Sons, New York/London (1962)

    Google Scholar 

  214. Nakai, Y.: Non-degenerate divisors on an algebraic surface. J. Sci. Hiroshima Univ. 24, 1–6 (1960)

    MathSciNet  MATH  Google Scholar 

  215. Nakai, Y.: A criterion of an ample sheaf on a projective scheme. Am. J. Math. 85, 14–26 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  216. Nakai, Y.: Some fundamental lemmas on projective schemes. Trans. Am. Math. Soc. 109, 296–302 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  217. Nakamura, I.: Moduli and Deformation Theory (Japanese), Have Fun with Mathematics 20, pp. 38–53. Nippon Hyoron Sha Co. Tokyo (2000)

    Google Scholar 

  218. Nakano, S.: On complex analytic vector bundles. J. Math. Soc. Jpn. 7, 1–12 (1955)

    Article  MATH  MathSciNet  Google Scholar 

  219. Nakano, S.: On the inverse of monoidal transformation. Publ. Res. Inst. Math. Sci. 6, 483–502 (1970/1971)

    Google Scholar 

  220. Nakano, S.: Vanishing theorems for weakly 1-complete manifolds. II. Publ. Res. Inst. Math. Sci. 10, 101–110 (1974/1975)

    Google Scholar 

  221. Nakano, S., Ohsawa, T.: Strongly pseudoconvex manifolds and strongly pseudoconvex domains. Publ. Res. Inst. Math. Sci. 20, 705–715 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  222. Nakano, S., Rhai, T.-S.: Vector bundle version of Ohsawa’s finiteness theorems. Math. Jpn. 24, 657–664 (1979/1980)

    Google Scholar 

  223. Narasimhan, R.: Sur les espaces complexes holomorphiquement complets. C. R. Acad. Sci. Paris 250, 3560–3561 (1960)

    MathSciNet  MATH  Google Scholar 

  224. Nemirovski, S.: Stein domains with Levi-plane boundaries on compact complex surfaces. Mat. Zametki 66, 632–635 (1999); translation in Math. Notes 66(3–4), 522–525 (1999/2000)

    Google Scholar 

  225. Nishino, T.: Sur une propriété des familles de fonctions analytiques de deux variables complexes. J. Math. Kyoto Univ. 4, 255–282 (1965)

    MathSciNet  MATH  Google Scholar 

  226. Nishino, T.: L’existence d’une fonction analytique sur une variété analytique complexe à deux dimensions. Publ. Res. Inst. Math. Sci. 18, 387–419 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  227. Nishino, T.: L’existence d’une fonction analytique sur une variété analytique complexe à dimension quelconque. Publ. Res. Inst. Math. Sci. 19, 263–273 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  228. Noguchi, J.: Analytic function theory of several variables —Elements of Oka’s coherence, preprint

    Google Scholar 

  229. Ohsawa, T.: A counter example of ampleness of positive line bundles. Proc. Jpn. Acad. Ser. A Math. Sci. 55, 193–194 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  230. Ohsawa, T.: Finiteness theorems on weakly 1-complete manifolds. Publ. Res. Inst. Math. Sci. 15, 853–870 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  231. Ohsawa, T.: On complete Kähler domains with C 1-boundary. Publ. Res. Inst. Math. Sci. 16, 929–940 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  232. Ohsawa, T.: Analyticity of complements of complete Kähler domains. Proc. Jpn. Acad. Ser. A Math. Sci. 56, 484–487 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  233. Ohsawa, T.: On H p, q(X, B) of weakly 1-complete manifolds. Publ. Res. Inst. Math. Sci. 17, 113–126 (1981)

    Google Scholar 

  234. Ohsawa, T.: A reduction theorem for cohomology groups of very strongly q-convex Kähler manifolds. Invent. Math. 63, 335–354 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  235. Ohsawa, T.: Addendum to: “A reduction theorem for cohomology groups of very strongly q-convex Kähler manifolds” (Invent. Math. 63(2), 335–354 (1981)). Invent. Math. 66, 391–393 (1982)

    Google Scholar 

  236. Ohsawa, T.: Isomorphism theorems for cohomology groups of weakly 1-complete manifolds. Publ. Res. Inst. Math. Sci. 18, 191–232 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  237. Ohsawa, T.: Vanishing theorems on complete Kähler manifolds. Publ. Res. Inst. Math. Sci. 20, 21–38 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  238. Ohsawa, T.: Completeness of noncompact analytic spaces. Publ. Res. Inst. Math. Sci. 20, 683–692 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  239. Ohsawa, T.: Hodge spectral sequence on compact Kähler spaces. Publ. Res. Inst. Math. Sci. 23, 265–274 (1987). Supplement: Publ. Res. Inst. Math. Sci. 27, 505–507 (1991)

    Google Scholar 

  240. Ohsawa, T.: Hodge spectral sequence and symmetry on compact Kähler spaces. Publ. Res. Inst. Math. Sci. 23, 613–625 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  241. Ohsawa, T.: On the infinite dimensionality of the middle L 2 cohomology of complex domains. Publ. Res. Inst. Math. Sci. 25, 499–502 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  242. Ohsawa, T.: Intersection cohomology – where L 2 theory meets the mixed Hodge theory (Japanese). In: Research on Complex Analytic Geometry and Related Topics, RIMS Kokyuroku, vol. 693, pp. 23–40. Research Institute for Mathematical Sciences, Kyoto (1989)

    Google Scholar 

  243. Ohsawa, T.: Cheeger-Goreski [Goresky]-MacPherson’s conjecture for the varieties with isolated singularities. Math. Z. 206, 219–224 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  244. Ohsawa, T.: On the L 2 cohomology groups of isolated singularities. In: Progress in Differential Geometry. Advanced Studies in Pure Mathematics, vol. 22, pp. 247–263. Mathematical Society of Japan, Tokyo (1993)

    Google Scholar 

  245. Ohsawa, T.: On the Bergman kernel of hyperconvex domains. Nagoya Math. J. 129, 43–52 (1993). Addendum, Nagoya Math. J. 137, 145–148 (1995)

    Google Scholar 

  246. Ohsawa, T.: On the extension of L 2 holomorphic functions III. Negligible weights. Math. Z. 219, 215–225 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  247. Ohsawa, T.: Pseudoconvex domains in \(\mathbb{P}^{n}\): a question on the 1-convex boundary points. In: Analysis and Geometry in Several Complex Variables, Katata, 1997. Trends in Mathematics, pp. 239–252. Birkhäuser, Boston (1999)

    Google Scholar 

  248. Ohsawa, T.: On the extension of L 2 holomorphic functions V. Effect of generalization. Nagoya Math. J. 161, 1–21 (2001)

    MathSciNet  MATH  Google Scholar 

  249. Ohsawa, T.: A precise L 2 division theorem. In: Complex Geometry, Göttingen, 2000, pp. 185–191. Springer, Berlin (2002)

    Google Scholar 

  250. Ohsawa, T.: Analysis of Several Complex Variables (Translated from the Japanese by Shu Gilbert Nakamura). Translations of Mathematical Monographs, vol. 211. Iwanami Series in Modern Mathematics, xviii+121 pp. American Mathematical Society, Providence (2002)

    Google Scholar 

  251. Ohsawa, T.: On the complement of Levi-flats in Kähler manifolds of dimension ≥ 3. Nagoya Math. J. 185, 161–169 (2007)

    MathSciNet  MATH  Google Scholar 

  252. Ohsawa, T.: A remark on pseudoconvex domains with analytic complements in compact Kähler manifolds. J. Math. Kyoto Univ. 47, 115–119 (2007)

    MathSciNet  MATH  Google Scholar 

  253. Ohsawa, T.: A reduction theorem for stable sets of holomorphic foliations on complex tori. Nagoya Math. J. 195, 41–56 (2009)

    MathSciNet  MATH  Google Scholar 

  254. Ohsawa, T.: A tower of Riemann surfaces whose Bergman kernels jump at the roof. Publ. Res. Inst. Math. Sci. 46, 473–478 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  255. Ohsawa, T.: Hartogs type extension theorems on some domains in Kähler manifolds. Ann. Polon. Math. 106, 243–254 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  256. Ohsawa, T.: On the complement of effective divisors with semipositive normal bundle. Kyoto J. Math. 52, 503–515 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  257. Ohsawa, T.: On projectively embeddable complex-foliated structures. Publ. Res. Inst. Math. Sci. 48, 735–747 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  258. Ohsawa, T.: Nonexistence of certain Levi flat hypersurfaces in Kähler manifolds from the viewpoint of positive normal bundles. Publ. Res. Inst. Math. Sci. 49, 229–239 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  259. Ohsawa, T.: Classification of real analytic Levi flat hypersurfaces of 1-concave type in Hopf surfaces. Kyoto J. Math. 54, 547–553 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  260. Ohsawa, T.: A lemma on Hartogs function and application to Levi flat hypersurfaces in Hopf surfaces, to appear in Prog. Math. 38 (2015)

    Google Scholar 

  261. Ohsawa, T.: Stability of pseudoconvexity of disc bundles over compact Riemann surfaces and application to a family of Galois coverings. Int. J. Math. 26, 1540003 (2015), [7 pages] doi:10.1142/S0129167X15400030

    Article  MathSciNet  MATH  Google Scholar 

  262. Ohsawa, T.: Application and simplified proof of a sharp L 2 extension theorem, to appear in Nagoya Math. J.

    Google Scholar 

  263. Ohsawa, T.: A remark on Hörmander’s isomorphism, to appear in proceedings of KSCV 10

    Google Scholar 

  264. Ohsawa, T.: Some updates of extension theorems by the L 2 estimates for \(\bar{\partial }\), submitted for publication

    Google Scholar 

  265. Ohsawa, T., Sibony, N.: Bounded p.s.h. functions and pseudoconvexity in Kähler manifold. Nagoya Math. J. 149, 1–8 (1998)

    Google Scholar 

  266. Ohsawa, T., Takegoshi, K.: On the extension of L 2 holomorphic functions. Math. Z. 195, 197–204 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  267. Ohsawa, T., Takegoshi, K.: Hodge spectral sequence on pseudoconvex domains. Math. Z. 197, 1–12 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  268. Oikawa, K., Sario, L.: Capacity Functions. Die Grundlehren der mathematischen Wissenschaften, Band 149, xvii+361 pp. Springer, New York (1969)

    Google Scholar 

  269. Oka, K.: Sur les fonctions analytiques de plusieurs variables VI. Domaines pseudoconvexes. Tôhoku Math. J. 49, 15–52 (1942)

    MathSciNet  MATH  Google Scholar 

  270. Oka, K.: Sur les fonctions analytiques de plusieurs variables VII. Sur quelques notions arithmétiques. Bull. Soc. Math. Fr. 78, 1–27 (1950)

    MathSciNet  MATH  Google Scholar 

  271. Oka, K.: Sur les fonctions analytiques de plusieurs variables VIII. Lemme fondamental. J. Math. Soc. Jpn. 3, 204–214 and 259–278 (1951)

    Google Scholar 

  272. Oka, K.: Sur les fonctions analytiques de plusieurs variables IX. Domaines finis sans point critique intérieur. Jpn. J. Math. 23, 97–155 (1953)

    MathSciNet  MATH  Google Scholar 

  273. Păun, M.: Siu’s invariance of plurigenera: a one-tower proof. J. Differ. Geom. 76, 485–493 (2007)

    MATH  Google Scholar 

  274. Pflug, P.: Quadratintegrable holomorphe Funktionen und die Serre-Vermutung. Math. Ann. 216, 285–288 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  275. Pjateckii-Shapiro, I.I.: Géométrie des domaines classiques et théorie des fonctions automorphes, Traduit du Russe par A. W. Golovanoff. Travaux et Recherches Mathêmatiques, No. 12, iv+160 pp. Dunod, Paris (1966)

    Google Scholar 

  276. Ramanujam, C.P.: Remarks on the Kodaira vanishing theorem. J. Indian Math. Soc. 36, 41–51 (1972)

    MathSciNet  MATH  Google Scholar 

  277. Ramanujam, C.P.: Supplement to the article “Remarks on the Kodaira vanishing theorem”. J. Indian Math. Soc. 38, 121–124 (1974)

    MathSciNet  MATH  Google Scholar 

  278. Raynaud, M.: Contre-exemple au “vanishing theorem” en caractêristique p > 0, C. P. Ramanujam – a tribute, 273–278, Tata Inst. Fund. Res. Studies in Math., vol. 8. Springer, Berlin/New York (1978)

    Google Scholar 

  279. Reider, I.: Vector bundles of rank 2 and linear systems on algebraic surfaces. Ann. Math. 127, 309–316 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  280. Remmert, R.: Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes. C. R. Acad. Sci. Paris 243, 118–121 (1956)

    MathSciNet  MATH  Google Scholar 

  281. Remmert, R.: From Riemann surfaces to complex spaces. In: Matériaux pour l’histoire des mathématiques au XXe siècle, Nice, 1996. Sémin. Congr., vol. 3, pp. 203–241. Société Mathématique de France, Paris (1998)

    Google Scholar 

  282. Remmert, R., Stein, K.: Über die wesentlichen Singularitäten analytischer Mengen. Math. Ann. 126, 263–306 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  283. Rhodes, J.A.: Sequences of metrics on compact Riemann surfaces. Duke Math. J. 72, 725–738 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  284. Richberg, R.: Stetige streng pseudokonvexe Funktionen. Math. Ann. 175, 257–286 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  285. Rothstein, W.: Zur Theorie der Analytischen Mannigfaltigkeiten im Raume von n komplexen Veränderlichen. Math. Ann. 129, 96–138 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  286. Saito, M.: Mixed Hodge modules. Publ. Res. Inst. Math. Sci. 26, 221–333 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  287. Sakai, A.: Uniform approximation on totally real sets. Math. Ann. 253, 139–144 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  288. Saper, L.: L 2-cohomology and intersection homology of certain algebraic varieties with isolated singularities. Invent. Math. 82, 207–256 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  289. Saper, L., Stern, M.: L 2-cohomology of arithmetic varieties. Proc. Natl. Acad. Sci. U.S.A. 84, 5516–5519 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  290. Sario, L., Oikawa, K.: Capacity Functions. Die Grundlehren der mathematischen Wissenschaften, Band 149, xvii+361 pp. Springer, New York (1969)

    Google Scholar 

  291. Satake, I.: Compactifications, old and new (translation of Sūgaku 51, 129–141). Sugaku Expositions 14, 175–189 (2001)

    Google Scholar 

  292. Scherk, J.: On the monodromy theorem for isolated hypersurface singularities, Invent. Math. 58, 289–301 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  293. Schoutens, H.: A non-standard proof of the Briançon-Skoda theorem. Proc. Am. Math. Soc. 131, 103–112 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  294. Schürmann, J.: Embeddings of Stein spaces into affine spaces of minimal dimension. Math. Ann. 307, 381–399 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  295. Seip, K.: Density theorems for sampling and interpolation in the Bargmann-Fock space I. J. Reine Angew. Math. 429, 91–106 (1992)

    MathSciNet  MATH  Google Scholar 

  296. Seip, K.: Beurling type density theorems in the unit disk. Invent. Math. 113, 21–39 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  297. Seip, K., Wallstén, R.: Density theorems for sampling and interpolation in the Bargmann-Fock space II. J. Reine Angew. Math. 429, 107–113 (1992)

    MathSciNet  MATH  Google Scholar 

  298. Serre, J.-P.: Quelques problèmes globaux relatifs aux variétés de Stein, Colloque sur les fonctions de plusieurs variables, Bruxelles, pp. 53–68 (1953)

    Google Scholar 

  299. Serre, J.-P.: Un théorème de dualité. Comment. Math. Helv. 29, 9–26 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  300. Shafarevich, I.R.: Basic Algebraic Geometry (Translated from the Russian by K. A. Hirsch). Die Grundlehren der mathematischen Wissenschaften, Band 213, xv+439 pp. Springer, New York/Heidelberg (1974)

    Google Scholar 

  301. Shcherbina, N.: Pluripolar graphs are holomorphic. Acta Math. 194, 203–216 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  302. Siu, Y.-T.: Analytic sheaf cohomology groups of dimension n of n-dimensional noncompact complex manifolds. Pac. J. Math. 28, 407–411 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  303. Siu, Y.-T.: Techniques of Extension of Analytic Objects. Lecture Notes in Pure and Applied Mathematics, vol. 8, iv+256 pp. Marcel Dekker, New York (1974)

    Google Scholar 

  304. Siu, Y.-T.: Characterization of privileged polydomains. Trans. Am. Math. Soc. 193, 329–357 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  305. Siu, Y.-T.: Analyticity of sets associated to Lelong numbers and the extension of closed positive currents. Invent. Math. 27, 53–156 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  306. Siu, Y.-T.: Complex-analyticity of harmonic maps, vanishing and Lefschetz theorems. J. Differ. Geom. 17, 55–138 (1982)

    MathSciNet  MATH  Google Scholar 

  307. Siu, Y.-T.: The Fujita conjecture and the extension theorem of Ohsawa-Takegoshi. In: Geometric Complex Analysis, Hayama, 1995, pp. 577–592. World Scientific Publishing, River Edge (1996)

    Google Scholar 

  308. Siu, Y.-T.: Invariance of plurigenera. Invent. Math. 134, 661–673 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  309. Siu, Y.-T.: Nonexistence of smooth Levi-flat hypersurfaces in complex projective spaces of dimension ≥ 3. Ann. Math. 151, 1217–1243 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  310. Siu, Y.-T.: Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type. In: Complex Geometry, Göttingen, 2000, pp. 223–277. Springer, Berlin (2002)

    Google Scholar 

  311. Siu, Y.-T.: Some recent transcendental techniques in algebraic and complex geometry. In: Proceedings of the International Congress of Mathematicians, Beijing, 2002, vol. I, pp. 439–448. Higher Education Press, Beijing (2002)

    Google Scholar 

  312. Siu, Y.-T.: Multiplier ideal sheaves in complex and algebraic geometry. Sci. China Ser. A 48(suppl.), 1–31 (2005)

    Google Scholar 

  313. Siu, Y.-T.: Finite generation of canonical ring by analytic method. Sci. China Ser. A 51, 481–502 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  314. Siu, Y.T., Yau, S.T.: Compact Kähler manifolds of positive bisectional curvature. Invent. Math. 59, 189–204 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  315. Stout, E.L.: Polynomial Convexity. Progress in Mathematics, vol. 261, xii+439 pp. Birkhäuser, Boston (2007)

    Google Scholar 

  316. Skoda, H.: Sous-ensembles analytiques d’ordre fini ou infini dans \(\mathbb{C}^{n}\). Bull. Soc. Math. Fr. 100, 353–408 (1972)

    MathSciNet  MATH  Google Scholar 

  317. Skoda, H.: Application des techniques L 2 à la théorie des idéaux d’une algèbre de fonctions holomorphes avec poids. Ann. Sci. École Norm. Sup. 5, 545–579 (1972)

    MathSciNet  MATH  Google Scholar 

  318. Skoda, H.: Fibrés holomorphes à base et à fibre de Stein. Invent. Math. 43, 97–107 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  319. Skoda, H.: Morphismes surjectifs de fibrés vectoriels semi-positifs. Ann. Sci. École Norm. Sup. 11, 577–611 (1978)

    MathSciNet  MATH  Google Scholar 

  320. Skoda, H.: Problem Session of the Conference on Complex Analysis, pp. 1–3 (2005). www.institut.math.jussieu.fr/projets/...skoda/probleme.Skoda

  321. Suita, N.: Capacities and kernels on Riemann surfaces. Arch. Ration. Mech. Anal. 46, 212–217 (1972)

    Article  MathSciNet  MATH  Google Scholar 

  322. Suita, N.: Modern Function Theory II, (POD edition). Morikita Publishing (2011) (Japanese)

    Google Scholar 

  323. Suzuki, O.: Pseudoconvex domains on a Kähler manifold with positive holomorphic bisectional curvature. Publ. Res. Inst. Math. Sci. 12, 191–214 (1976/1977). Supplement: Publ. Res. Inst. Math. Sci. 12, 439–445 (1976/1977)

    Google Scholar 

  324. Sznajdman, J.: An elementary proof of the Briançon-Skoda theorem. Annales de la facult é des sciences de Toulouse Sér. 6 19, 675–685 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  325. Takayama, S.: Adjoint linear series on weakly 1-complete Kähler manifolds. I. Global projective embedding. Math. Ann. 311, 501–531 (1998)

    MathSciNet  MATH  Google Scholar 

  326. Takayama, S.: Adjoint linear series on weakly 1-complete Kähler manifolds. II. Lefschetz type theorem on quasi-abelian varieties. Math. Ann. 312, 363–385 (1998)

    MathSciNet  MATH  Google Scholar 

  327. Takayama, S.: The Levi problem and the structure theorem for non-negatively curved complete Kähler manifolds. J. Reine Angew. Math. 504, 139–157 (1998)

    MathSciNet  MATH  Google Scholar 

  328. Takegoshi, K.: A generalization of vanishing theorems for weakly 1-complete manifolds. Publ. Res. Inst. Math. Sci. 17, 311–330 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  329. Takegoshi, K.: Relative vanishing theorems in analytic spaces. Duke Math. J. 52, 273–279 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  330. Takeuchi, A.: Domaines pseudoconvexes infinis et la métrique riemannienne dans un espace projectif. J. Math. Soc. Jpn. 16, 159–181 (1964)

    Article  MATH  Google Scholar 

  331. Takeuchi, A.: Domaines pseudoconvexes sur les variétés kählériennes. J. Math. Kyoto Univ. 6, 323–357 (1967)

    MathSciNet  MATH  Google Scholar 

  332. Tian, G.: On a set of polarized Kähler metrics on algebraic manifolds. J. Differ. Geom. 32, 99–130 (1990)

    MATH  Google Scholar 

  333. Ueda, T.: On the neighborhood of a compact complex curve with topologically trivial normal bundle. J. Math. Kyoto Univ. 22, 583–607 (1982/1983)

    Google Scholar 

  334. Ueda, T.: Pseudoconvex domains over Grassmann manifolds. J. Math. Kyoto Univ. 20, 391–394 (1980)

    MathSciNet  MATH  Google Scholar 

  335. Varouchas, J.: Stabilité de la classe des variétés kählériennes par certains morphismes propres. Invent. Math. 77, 117–127 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  336. Viehweg, E.: Vanishing theorems. J. Reine Angew. Math. 335, 1–8 (1982)

    MathSciNet  MATH  Google Scholar 

  337. Vogt, C.: Two renarks concerning toroidal groups. Manuscr. Math. 41, 217–232 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  338. Wall, C.T.C.: Lectures on C ∞–stability and classification. In: Proceedings of Liverpool Singularities Symposium I (1969/1970). Lecture Notes in Mathematics, vol. 192, pp. 178–206. Springer, Berlin (1971)

    Google Scholar 

  339. Weil, A.: Sur la théorie des formes différentielles attachées à une variété analytique complexe. Comment. Math. Helv. 20, 110–116 (1947)

    Article  MathSciNet  MATH  Google Scholar 

  340. Weil, A.: Introduction à l’étude des variétés kählériennes, Publications de l’Institut de Mathématique de l’Université de Nancago, VI. Actualités Sci. Ind. no. 1267, 175 p. Hermann, Paris (1958)

    Google Scholar 

  341. Wells, R.O., Jr.: Differential Analysis on Complex Manifolds, 3rd edn. With a new appendix by Oscar Garcia-Prada. Graduate Texts in Mathematics, vol. 65. Springer, New York (2008)

    Google Scholar 

  342. Weyl, H.: The method of orthogonal projection in potential theory. Duke Math. J. 7, 411–444 (1940)

    Article  MathSciNet  MATH  Google Scholar 

  343. Weyl, H.: David Hilbert and his mathematical work. Bull. Am. Math. Soc. 50, 612–654 (1944)

    Article  MathSciNet  MATH  Google Scholar 

  344. Wiener, N.: Certain notions in potential theory. J. Math. MIT 3, 24–51 (1924)

    MATH  Google Scholar 

  345. Wu, H.: An elementary method in the study of nonnegative curvature. Acta Math. 142, 57–78 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  346. Yamaguchi, H.: Sur le mouvement des constantes de Robin. J. Math. Kyoto Univ. 15, 53–71 (1975)

    MathSciNet  MATH  Google Scholar 

  347. Yamaguchi, H.: Parabolicité d’une fonction entiere. J. Math. Kyoto Univ. 16, 71–92 (1976)

    MathSciNet  MATH  Google Scholar 

  348. Yamaguchi, H.: Variations of pseudoconvex domains over \(\mathbb{C}^{n}\). Mich. Math. J. 36, 415–457 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  349. Yau, S.-T.: A general Schwarz lemma for Kähler manifolds. Am. J. Math. 100, 197–203 (1978)

    Article  MATH  Google Scholar 

  350. Yau, S.-T.: Nonlinear analysis in geometry. l’Enseignement Math. 33, 109–158 (1986)

    Google Scholar 

  351. Zarankiewicz, K.: Über ein numerishces Verfahren zur konformen Abbildung zweifach zusammenhängender Gebiete. Z. Angew. Math. Mech. 14, 97–104 (1934)

    Article  MATH  Google Scholar 

  352. Zelditch, S.: Szegö kernels and a theorem of Tian. Int. Math. Res. Not. 6, 317–331 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  353. Zucker, S.: Hodge theory with degenerating coefficients, L 2-cohomology in the Poincaré metric. Ann. Math. 109, 415–476 (1979)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, Japan

    Takeo Ohsawa

Authors
  1. Takeo Ohsawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Japan

About this chapter

Cite this chapter

Ohsawa, T. (2015). Basic Notions and Classical Results. In: L² Approaches in Several Complex Variables. Springer Monographs in Mathematics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55747-0_1

Download citation

Publish with us

Policies and ethics

Search

Navigation