• Robert E. Greene
  • Kang-Tae Kim
  • Steven G. Krantz
Part of the Progress in Mathematics book series (PM, volume 291)


Many of the results in previous chapters concerned bounded strongly pseudoconvex domains in complex Euclidean spaces. As it happens, almost all of these results can be extended in some form to more general situations. In particular, most of them apply in some suitable form to strongly pseudoconvex domains with compact closure in Stein manifolds. The restriction to the Euclidean space case earlier simplified the statements and made for a clearer exposition of the proof techniques. But it is of course important to realize that generalizations are possible when indeed they are possible. In this final chapter, we shall try to indicate these possibilities in enough detail that interested readers will be able to carry through the detailed statements and proofs for themselves in the more general situations which will be indicated.


Holomorphic Function Pseudoconvex Domain Bergman Kernel Stein Manifold Holomorphic Sectional Curvature 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Robert E. Greene
    • 1
  • Kang-Tae Kim
    • 2
  • Steven G. Krantz
    • 3
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsPohang Institute of Science and TechnologyPohangSouth Korea
  3. 3.Department of MathematicsWashington UniversitySt. LouisUSA

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