- Full Description
This work examines a rich tapestry of themes and concepts and provides a comprehensive treatment of an important area of mathematics, while simultaneously covering a broader area of the geometry of domains in complex space. At once authoritative and accessible, this text touches upon many important parts of modern mathematics: complex geometry, equivalent embeddings, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces.The Geometry of Complex Domains can serve as a “coming of age” book for a graduate student who has completed at least one semester or more of complex analysis, and will be most welcomed by analysts and geometers engaged in current research.
- Table of Contents
Table of Contents
- 1 Preliminaries.
- 2 Riemann Surfaces and Covering Spaces.
- 3 The Bergman Kernel and Metric.
- 4 Applications of Bergman Geometry.
- 5 Lie Groups Realized as Automorphism Groups.
- 6 The Significance of Large Isotropy Groups.
- 7 Some Other Invariant Metrics.
- 8 Automorphism Groups and Classification of Reinhardt Domains.
- 9 The Scaling Method, I.
- 10 The Scaling Method, II.
- 11 Afterword.
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