The Geometry of Complex Domains

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.

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.