Apress

The Geometry of Complex Domains

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

The Geometry of Complex Domains Cover Image

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

  • ISBN13: 978-0-8176-4139-9
  • 317 Pages
  • Publication Date: May 18, 2011
  • Available eBook Formats: PDF
  • eBook Price: $99.00
Buy eBook Buy Print Book Add to Wishlist
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

If you think that you've found an error in this book, please let us know about it. You will find any confirmed erratum below, so you can check if your concern has already been addressed.

* Required Fields

No errata are currently published