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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.
List of contents
Preface.- 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.- Bibliography.- Index.
About the author
Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series. He lives in St. Louis, Missouri.
Summary
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.
Additional text
From the reviews:
“The book under review gives an excellent presentation of modern problems related to various characterizations of the holomorphic geometry of domains in Cn and complex manifolds. … The book may be strongly recommended for researchers and Ph.D. students working in complex analysis.” (Marek Jarnicki, Mathematical Reviews, Issue 2012 c)
Report
From the reviews:
"The book under review gives an excellent presentation of modern problems related to various characterizations of the holomorphic geometry of domains in Cn and complex manifolds. ... The book may be strongly recommended for researchers and Ph.D. students working in complex analysis." (Marek Jarnicki, Mathematical Reviews, Issue 2012 c)
