Characterizations of certain weakly pseudoconvex domains with non-compact automorphism groups

  • Robert E. Greene
  • Steven G. Krantz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1268)


Real Hypersurface Pseudoconvex Domain Bergman Kernel Levi Form Biholomorphic Mapping 
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.
    F. Beatrous and R.M. Range, On holomorphic approximation in weakly pseudoconvex domains, Pac. Jour. Math. 89(1980), 249–255.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    S.R. Bell, Biholomorphic mappings and the \(\bar \partial \) problem, Annals of Math. 114(1981), 103–113.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    T. Bloom and I. Graham, A geometric characterization of points of finite type, J. Diff. Geom. 12(1977), 171–182.MathSciNetzbMATHGoogle Scholar
  4. 4.
    R. Braun, W. Karp and H. Upmeier, On the automorphisms of circular domains in complex Banach spaces, Manuscripta Math. 25(1978), 97–133.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    D. Burns, S. Shnider, R. Wells, On deformations of strictly pseudoconvex domains, Inventiones Math. 46(1978), 237–253.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    S. Chern and J. Moser, Real hypersurfaces in complex manifolds, Acta Math. 133(1974), 219–271.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. 115(1982), 615–637.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    I. Graham, Boundary behavior of the Caratheodary and Kobayashi metrics on strongly pseudoconvex domains in ℂn with smooth boundary, Trans. Am. Math. Soc. 207(1975), 219–240.zbMATHGoogle Scholar
  9. 9.
    R. Greene and S. Krantz, Stability of the Bergman kernel and curvature properties of bounded domains, Proceedings of the Princeton Conference on Several Complex Variables, Princeton University Press, Princeton, 1981.Google Scholar
  10. 10.
    R. Greene and S. Krantz, Deformations of complex structures, estimates for the \(\bar \partial \) equation, and stability of the Bergman kernel, Adv. Math. 43(1982), 1–86.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    R. Greene and S. Krantz, The automorphism groups of strongly pseudoconvex domains, Math. Ann. 261(1982), 425–466.MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    R. Greene and S. Krantz, The stability of the Bergman kernel and the geometry of the Bergman metric, Bull. Am. Math. Soc. (New Series) 4(1981), 111–115.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    R. Greene and S. Krantz, Stability of the Caratheodary and Kobayashi metrics and applications to biholomorphic mappings, Proceedings of Symposia in Pure Mathematics 41(1984), American Mathematical Society, Providence, pp. 77–93.Google Scholar
  14. 14.
    R. Greene and S. Krantz, Normal families and the semicontinuity of isometry and automorphism groups, Math. Z. 190(1985), 455–467.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    G.M. Henkin and Leinterer, Theory of functions of strictly pseudoconvex sets with non-smooth boundary, Report of the Akadamie der Wissenschaften der DDR, Berlin, 1981.Google Scholar
  16. 16.
    L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983.zbMATHGoogle Scholar
  17. 17.
    N. Kerzman, Hölder and Lp solutions for the equation % Mat\(\bar \partial u = f\) on strongly pseudoconvex domains, Comm. Pure Appl. Math. XXIV (1971), 301–380.MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    J. Kohn, Boundary behavior of \(\bar \partial \) on weakly pseudoconvex manifolds of dimension two, J. Diff. Geom. 6(1972), 523–542.MathSciNetzbMATHGoogle Scholar
  19. 19.
    J. Kohn, Global regularity for \(\bar \partial \) on weakly pseudoconvex manifolds, Trans. A.M.S. 181(1973), 273–292.MathSciNetzbMATHGoogle Scholar
  20. 20.
    J. Kohn, Subellipticity of the \(\bar \partial \)-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142(1979), 79–122.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    W. Koppelman, The Cauchy integral formula for functions of several complex variables, Bull. Am. Math. Soc. 73(1967), 373–377.MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    S. Krantz, Function Theory of Several Complex Variables, John Wiley and and Sons, New York, 1982.zbMATHGoogle Scholar
  23. 23.
    R. Narasimhan, Several Complex Variables, University of Chicago Press, Chicago, 1971.zbMATHGoogle Scholar
  24. 24.
    R.M. Range, The Caratheodary metric and holomorphic maps on a class of weakly pseudoconvex domains, Pac. Jour. Math. 78(1978), 173–189.MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Reiffen, Die differnetialgeometrischen Eigenschaften der invarianten Distanzfunktion von Caratheodory, Schr. Math. Inst. Univ. 26(1963).Google Scholar
  26. 26.
    J. Rosay, Sur une characterization de la boule parmi son groupe d'automorphismes, Ann. Inst. Four. Grenbole XXIX (1979), 91–97.MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    W. Rudin, Function Theory in the Unit Ball of Cn, Springer Verlag, Berlin, 1980.CrossRefzbMATHGoogle Scholar
  28. 28.
    T. Sunada, Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235(1978), 111–128.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    N. Tanaka, On generalized graded Lie algebras and geometric structures I, J. Math. Soc. Japan 19(1967), 215–254.MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    B. Wong, Characterization of the ball in Cn by its automorphism group, Invent. Math. 41(1977), 253–257.MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    H. Wu, Normal families of holomorphic mappings, Acta Math. 119(1967), 193–233.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Robert E. Greene
  • Steven G. Krantz

There are no affiliations available

Personalised recommendations