Geometry of holomorphic mappings
- united States of America -- (Springer) -- 2023
- xi, 213p.
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
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.