The Resource The geometry of complex domains, Robert E. Greene, Kang-Tae Kim, Steven G. Krantz

The geometry of complex domains, Robert E. Greene, Kang-Tae Kim, Steven G. Krantz

The geometry of complex domains
The geometry of complex domains
Statement of responsibility
Robert E. Greene, Kang-Tae Kim, Steven G. Krantz
Cataloging source
Dewey number
index present
Literary form
non fiction
Nature of contents
Series statement
Progress in mathematics
Series volume
v. 291
The geometry of complex domains, Robert E. Greene, Kang-Tae Kim, Steven G. Krantz
Bibliography note
Includes bibliographical references and index
  • net
  • Contents note continued: 10.1.Klembeck's Theorem with Stability in the C2 Topology -- 10.2.Separating Boundary and Interior Points -- 10.3.Ian Graham's Theorem by Scaling -- 10.4.Proper Mappings Between Bounded Strongly Pseudoconvex Domains -- 11.Afterword
  • Contents note continued: 3.5.Stability of the Geometry of the Bergman Metric -- 3.6.Further Observations on the Geometric Stability of the Bergman Curvature -- 4.Applications of Bergman Geometry -- 4.1.Applications of Stability near the Boundary -- 4.2.Bergman Representative Coordinates -- 4.3.Equivariant Embedding and Concrete Realization of Abstract Complex Structures -- 4.4.Semicontinuity of Automorphism Groups -- 4.5.Obtaining a Stable Extension -- 5.Lie Groups Realized as Automorphism Groups -- 5.1.Introduction -- 5.2.General Philosophy -- 5.3.The Saerens/Zame Proof -- 5.4.The Bedford/Dadok Proof -- 6.The Significance of Large Isotropy Groups -- 6.1.Complex Manifolds with Large Isotropy at One Point -- 6.2.Proof of Theorem 6.1.1: An Invariant Metric -- 6.3.Proof of Theorem 6.1.1: Biholomorphisms of Metric Balls -- 6.4.Proof of Theorem 6.1.1, Assuming Lemma A -- 6.5.Statement and Discussion of Lemma A --
  • Contents note continued: 6.6.Alternative Viewpoints and the Modification for the Theorem in the Manifold Case -- 6.7.The Compact Manifold Case -- 7.Some Other Invariant Metrics -- 7.1.The Caratheodory Metric -- 7.2.The Kobayashi Metric and Distance -- 7.3.Riemann Surfaces and Curvature Conditions for Kobayashi Hyperbolicity -- 7.4.Remarks on Finsler Metrics and the CRF System -- 7.5.The Wu Metric -- 7.6.The Cheng-Yau Invariant Einstein-Kahler Metric -- 8.Automorphism Groups and Classification of Reinhardt Domains -- 8.1.Reinhardt Domains -- 8.2.Sunada's Work -- 8.3.Shimizu's Theorems -- 8.4.Non-Reinhardt Circular Domains -- 9.The Scaling Method, I -- 9.1.A Basic Example: Scaling Method in Dimension 1 -- 9.2.Higher Dimensional Scaling and the Wong-Rosay Theorem -- 9.3.A Theorem of Bedford and Pinchuk -- 9.4.Analytic Polyhedra with Noncompact Automorphism Group -- 9.5.The Greene-Krantz Conjecture -- 10.The Scaling Method, II --
  • Machine generated contents note: 1.Preliminaries -- 1.1.Automorphism Groups -- 1.2.Some Fundamentals from Complex Analysis of Several Variables -- 1.3.Normal Families and Automorphisms -- 1.4.The Basic Examples -- 1.5.Orbit Accumulation Boundary Points -- 1.6.Holomorphic Vector Fields and Their Flows -- 2.Riemann Surfaces and Covering Spaces -- 2.1.Coverings of Riemann Surfaces -- 2.2.Covering Spaces and Invariant Metrics, I: Quotients of C -- 2.3.Covering Spaces and Invariant Metrics, II: Quotients of D -- 2.4.Covering Spaces and Automorphisms in General -- 2.5.Compact Quotients of D and Their Automorphisms -- 2.6.The Automorphism Group of a Riemann Surface of Genus at Least 2 -- 2.7.Automorphisms of Multiply Connected Domains -- 3.The Bergman Kernel and Metric -- 3.1.The Bergman Space and Kernel -- 3.2.The Bergman Metric on Complex Manifolds -- 3.3.Examples of Bergman Kernels and Metrics -- 3.4.The Bergman Metric on Strongly Pseudoconvex Domains --
Control code
25 cm
xiv, 303 p.
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