The Geometry of Complex Domains [Hardcover]

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.

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.

This highly original work, written by the creators of the multivariable theory of automorphisms, is a rich tapestry of themes and concepts, and a comprehensive treatment of an important area of mathematics. From Poincar?'s work on biholomorphic inequivalence in 1906, it became clear that the structures of the automorphism groups of domains in multi-dimensional complex space are more complex, and more interesting, than those in the complex plane. The authors build on this theme and trace the evolution of the classical theory to the modern theory, which is today a cornerstone of geometric analysis.

The text begins with an introductory chapter on the concept of an automorphism group in which the theory in one complex variable is presented, emphasizing the classical ideas of Schwarz, Jobe, and others. Also examined is the theory of planar domains of multiple but finite connectivity, princlc