Several Complex Variables and the Geometry of

Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved).

Preface
Holomorphic Functions and Mappings	p. 1
Preliminaries	p. 1
Holomorphic mappings	p. 11
Further applications	p. 25
Basic analytic geometry	p. 31
Holomorphic Mappings and Local Algebra	p. 42
Finite analytic mappings	p. 42
Intersection numbers	p. 60
The order of contact of an ideal	p. 71
Higher order invariants	p. 85
Geometry of Real Hypersurfaces	p. 88
CR geometry	p. 88
Algebraic real hypersurfaces and complex varieties	p. 100
Real analytic subvarieties	p. 108
Points of Finite Type	p. 123
Orders of contact	p. 123
Local bounds	p. 135
Other finite type conditions	p. 141
Conclusions	p. 148
Proper Holomorphic Mappings Between Balls	p. 151
Rational proper mappings	p. 151
Invariance under fixed-point-free finite unitary groups	p. 171
Boundary behavior	p. 188
Geometry of the [actual symbol not reproducible]-Neumann Problem	p. 194
Introduction to the problem	p. 194
Existence and regularity results on the [actual symbol not reproducible] and [actual symbol not reproducible]-Neumann problems	p. 198
Subellipticity	p. 199
Subelliptic multipliers	p. 206
Varieties of positive holomorphic dimension	p. 225
Analysis on Finite Type Domains	p. 242
The Bergman projection	p. 242
Boundary invariants and CR mappings	p. 249
Problems	p. 254
Index of Notation	p. 261
Bibliography	p. 265
Index	p. 271
Table of Contents provided by Blackwell. All Rights Reserved.

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

FREE SHIPPING

Amazon no longer offers textbook rentals. We do!

Several Complex Variables and the Geometry of Real Hypersurfaces

Summary

Table of Contents

Supplemental Materials