TY  - GEN
AU  - Pinchuk, Sergey 
AU  - Shafikov, Rasul
AU  - Sukhov, Alexandre
TI  - Geometry of holomorphic mappings
SN  - 9783031371486
U1  - 515.98 PIN/G 
PY  - 2023///
CY  - united States of America -- 
PB  - (Springer) -- 
KW  - Mathematics
KW  - Analysis
KW  - Holomorphic mappings
N1  - 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

N2  - 
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
ER  -