The imbedding problem for open complex manifolds

  • J. S. Bland
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1268)


Finite Type Real Hypersurface Pseudoconvex Domain Bergman Kernel Stein Manifold 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bedford, E., Bell, S. and Catlin, D., "Boundary behavior of proper holomorphic mappings," Mich. Math. J. 30 (1983), 107–111.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bell, S., "Biholomorphic mappings and the ∂-problem," Ann. of Math. (2) 114 (1981), 103–133.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Bell, S. and Catlin D., "Boundary regularity of proper holomorphic mappings," Duke Math. J. 49 (1982), 385–396.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Bell, S. and Ligocka, E., "A simplification and extension of Fefferman's theorem on biholomorphic mappings," Invent. Math. 57 (1980), 283–289.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bishop, E., "Mappings of partially analytic spaces," Amer. J. Math. 83 (1961), 209–242.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Bland, J., "On the existence of bounded holomorphic functions on complete Kähler manifolds," Invent. Math. 81 (1985), 555–566.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bland, J., "The Einstein-Kähler metric on {|z|2+|w|2p < l}," Mich. Math. J. 33 (1986), 209–220.MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bland, J., "Bounded imbeddings of open Kähler manifolds in CN," preprint.Google Scholar
  9. 9.
    Bloom, T., and Graham, I., "A geometric characterization of points of type m on real hypersurfaces," J. Diff. Geom. 12 (1977), 171–182.MathSciNetzbMATHGoogle Scholar
  10. 10.
    Boutet de Monvel, L., "Integration des equations de Cauchy-Riemann induites formelles," Seminaire Goulaouic-Schwartz, 1974–75.Google Scholar
  11. 11.
    Burns, D., Diederich, K., and Schnider, S., "Distinguished curves in pseudoconvex boundaries," Duke Math. J. 44 (1977), 407–431.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Catlin, D., "Necessary conditions for subellipticity of the ∂-Neumann problem," Ann. of Math. 117 (1983), 147–171.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    _____, "Boundary invariants of pseudoconvex domains," Ann. of Math. 120 (1984), 529–586.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    _____, "Global regularity of the ∂-Neumann problem," Proc. Sym. Pure Math., vol. 41, Amer. Math. Soc., Providence, R.I. (1984), 39–49.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    _____, "Subelliptic estimates for the ∂-Neumann problem on pseudoconvex domains," preprint.Google Scholar
  16. 16.
    Cheng, S.Y., and Yau, S.-T., "On the existence of a Kähler metric on noncompact complex manifolds and the regularity of Fefferman's equations," Comm. Pure Appl. Math. 33 (1980), 507–544.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Chern, S.S. and Moser, J.K., "Real hypersurfaces in complex manifolds," Acta Math. 133 (1974), 219–271.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    D'Angelo, J., "Real hypersurfaces, orders of contact, and applications," Ann. of Math. (2) 115 (1982), 615–637.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    _____, "Finite type conditions for real hypersurfaces in Cn," preprint.Google Scholar
  20. 20.
    Diederich, K., and Fornaess, J.E., "Boundary regularity of proper holomorphic mappings," Invent. Math. 67 (1982), 363–384.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Fefferman, C., "The Bergman kernel and biholomorphic mappings of pseudoconvex domains," Invent. Math. 26 (1974), 1–65.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Fefferman, C., "Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains," Ann. of Math. 103 (1976), 395–416.MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Folland, G.B. and Kohn, J.J., "The Neumann problem for the Cauchy-Riemann complex," Ann. of Math. Studies, no. 75, Princeton Univ. Press, Princeton, N.J., 1972.zbMATHGoogle Scholar
  24. 24.
    Fornaess, J.E., "Biholomorphic mappings between weakly pseudoconvex domains," Pacific J. Math. 74 (1978), 63–65.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Grauert, H., "On Levi's problem and the imbedding of real analytic manifolds," Ann. of Math. 68 (1958), 460–472.MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Greene, R.E. and Wu, H., "Curvature and complex analysis. I, II, III," Bull. Amer. Math. Soc. 77 (1971) 1045–1049; ibid. 78 (1972), 866–870; 79 (1973), 606–608.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    _____, "On the subharmonicity and plurisubharmonicity of geodesically convex functions," Indiana Univ. Math. J. 22 (1973), 641–653.MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    _____, "Some function-theoretic properties of noncompact Kähler manifolds," Proc. Sym. Pure Math., vol. 27, part II, Amer. Math. Soc., Providence, R.I. (1975), 33–41.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    _____, "C convex functions and manifolds of positive curvature," Acta Math. 137 (1976), 209–245.MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    _____, "Analysis on noncompact Kähler manifolds," Proc. Sym. Pure Math., vol. 30, part II, Providence, R.I. (1977), 69–100.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    _____, "Gap theorems for noncompact Riemannian manifolds," Duke Math. J. 49 (1982), 731–756.MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Hörmander, L., "L2 estimates and existence theorems for the ∂ operator," Acta Math. 113 (1965), 89–152.MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Hörmander, L., "An introduction to complex analysis in several variables," Van Nostrand, Princeton, N.J. 1966.zbMATHGoogle Scholar
  34. 34.
    Klembeck, P., "Kähler metrics of negative curvature, the Bergman metric near the boundary and the Kobayashi metric on smooth bounded strictly pseudoconvex sets," Indiana Math. J. 27 (2) (1978), 275–282.MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Kohn, J.J., "Harmonic integrals on strongly pseudoconvex manifolds, I, II", Ann. of Math. (2) 78 (1963), 112–148; ibid. (2) 79 (1964), 450–472.MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    _____, "Boundary behaviour of ∂ on weakly pseudoconvex manifolds of dimension two," J. Diff. Geom. 6 (1972), 523–542.MathSciNetzbMATHGoogle Scholar
  37. 37.
    _____, "Global regularity for ∂ on weakly pseudoconvex manifolds," Trans. Amer. Math. Soc. 181 (1973), 273–292.MathSciNetzbMATHGoogle Scholar
  38. 38.
    _____, "Methods of partial differential equations," Proc. Sym. Pure Math., vol. 30, Part I, Amer. Math. Soc., Providence, R.I. (1977), 215–237.MathSciNetCrossRefGoogle Scholar
  39. 39.
    _____, "Subellipticity of the ∂-Neumann problem on pseudoconvex domains: Sufficient conditions," Acta Math. 142 (1979), 79–122.MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Kohn, J.J. and Nirenberg, L., "Noncoercive boundary value problems," Comm. Pure Appl. Math. 18 (1965), 443–492.MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Lempert, L., "La métrique de Kobayashi et la répresentation des domaine sur la boule," Bull. Soc. Math. France 109 (1981), 427–474.MathSciNetzbMATHGoogle Scholar
  42. 42.
    Mok, N., Siu, Y.T. and Yau, S.-T., "The Poincaré-Lelong equation on complete Kähler manifolds," Compositio Math. 44 (1981), no. 1–3, 183–218.MathSciNetzbMATHGoogle Scholar
  43. 43.
    Mok, N. and Yau, S.-T., "Completeness of the Kähler Einstein metric on bounded domains and the characterization of domains of holomorphy by curvature conditions," Proc. Sym. Pure Math., Vol. 39, Part I, Providence, R.I. (1983), 41–59.MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Narasimhan, R., "Imbedding of holomorphically complete complex spaces," Amer. J. Math. 82 (1960), 917–934.MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Remmert, R., "Sur les espaces analytiques holomorphiquement séparables et holomorphiquement convexes," C.R. Acad. Sci. Paris 243 (1956), 118–121.MathSciNetzbMATHGoogle Scholar
  46. 46.
    Rossi, H. and Taylor J., "On algebras of holomorphic functions on finite pseudoconvex manifolds," J. Functional Anal. 24 (1977), 11–31.MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Siu, Y.T., and Yau, S.-T., "Complete Kähler manifolds with nonpositive curvature of faster than quadratic decay," Ann. of Math. 105 (1977), 225–264.MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Webster, S., "Kähler metrics associated to a real hypersurface," Comment. Math. Helvetici 52 (1977), 235–250.MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Yau, S.-T., "Harmonic Functions on complete Riemannian manifolds," Comm. Pure Appl. Math. 28 (1975), 201–228.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • J. S. Bland
    • 1
  1. 1.University of TorontoTorontoCanada

Personalised recommendations