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The Geometry of Complex Domains

By Robert E. Greene , Kang-Tae Kim , Steven G. Krantz

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This highly original book examines a rich tapestry of themes and concepts, including complex geometry, Finsler metrics, Bergman and Kahler geometry, curvatures, differential invariants, boundary asymptotics of geometries, group actions, and moduli spaces.

Full Description

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  • ISBN13: 978-0-8176-4139-9
  • 317 Pages
  • Publication Date: May 18, 2011
  • Available eBook Formats: PDF
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. Preface.
  2. 1 Preliminaries.
  3. 2 Riemann Surfaces and Covering Spaces.
  4. 3 The Bergman Kernel and Metric.
  5. 4 Applications of Bergman Geometry.
  6. 5 Lie Groups Realized as Automorphism Groups.
  7. 6 The Significance of Large Isotropy Groups.
  8. 7 Some Other Invariant Metrics.
  9. 8 Automorphism Groups and Classification of Reinhardt Domains.
  10. 9 The Scaling Method, I.
  11. 10 The Scaling Method, II.
  12. 11 Afterword.
  13. Bibliography.
  14. Index.
Errata

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