Geometry of Holomorphic Mappings / by Sergey Pinchuk, Rasul Shafikov, Alexandre Sukhov.

Format:

Book

Author/Creator:

Pinchuk, Sergey.

Contributor:

Shafikov, Rasul.

Sukhov, Alexandre.

Series:

Frontiers in Mathematics, 1660-8054

Language:

English

Subjects (All):

Functions of complex variables.

Several Complex Variables and Analytic Spaces.

Functions of a Complex Variable.

Local Subjects:

Several Complex Variables and Analytic Spaces.

Functions of a Complex Variable.

Physical Description:

1 online resource (217 pages)

Edition:

1st ed. 2023.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2023.

Summary:

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.

Notes:

Description based on publisher supplied metadata and other sources.

Other Format:

Print version: Pinchuk, Sergey Geometry of Holomorphic Mappings

ISBN:

3-031-37149-6

OCLC:

1401055773