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Full Description
This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle.
Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
Contents
Chapter. 1. Preliminaries.- Chapter. 2. Why boundary regularity?.- Chapter. 3. Continuous extension of holomorphic mappings.- Chapter. 4. Boundary smoothness of holomorphic mappings.- Chapter. 5. Proper holomorphic mappings.- Chapter. 6. Uniformization of domains with large automorphism groups.- Chapter. 7. Local equivalence of real analytic hypersurfaces.- Chapter. 8. Geometry of real hypersurfaces: analytic continuation.- Chapter. 9. Segre varieties.- Chapter. 10. Holomorphic correspondences.- Chapter. 11. Extension of proper holomorphic mappings.- Chapter. 12. Extension in C2.- Appendix.- Bibliography.- Index.
