Real Submanifolds in Complex Space and Their Mappings (PMS-47) / M. Salah Baouendi, Linda Preiss Rothschild, Peter Ebenfelt.

Format:

Book

Author/Creator:

Baouendi, M. Salah, author.

Ebenfelt, Peter, author.

Rothschild, Linda Preiss, author.

Series:

Princeton Mathematical Series

Language:

English

Subjects (All):

Submanifolds.

Functions of several complex variables.

Physical Description:

1 online resource (418 p.)

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

This book presents many of the main developments of the past two decades in the study of real submanifolds in complex space, providing crucial background material for researchers and advanced graduate students. The techniques in this area borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic, and analytical geometry. In turn, these latter areas have been enriched over the years by the study of problems in several complex variables addressed here. The authors, M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, include extensive preliminary material to make the book accessible to nonspecialists. One of the most important topics that the authors address here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on real submanifolds. They present the main results in this area with a novel and self-contained approach. The book also devotes considerable attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. The authors also give a thorough comparison of the various nondegeneracy conditions for manifolds and mappings and present new geometric interpretations of these conditions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.

Contents:

Frontmatter

CONTENTS

PREFACE

CHAPTER I. HYPERSURFACES AND GENERIC SUBMANIFOLDS IN ℂN

CHAPTER II. ABSTRACT AND EMBEDDED CR STRUCTURES

CHAPTER III. VECTOR FIELDS: COMMUTATORS, ORBITS, AND HOMOGENEITY

CHAPTER IV. COORDINATES FOR GENERIC SUBMANIFOLDS

CHAPTER V. RINGS OF POWER SERIES AND POLYNOMIAL EQUATIONS

CHAPTER VI. GEOMETRY OF ANALYTIC DISCS

CHAPTER VII. BOUNDARY VALUES OF HOLOMORPHIC FUNCTIONS IN WEDGES

CHAPTER VIII. HOLOMORPHIC EXTENSION OF CR FUNCTIONS

CHAPTER IX. HOLOMORPHIC EXTENSION OF MAPPINGS OF HYPERSURFACES

CHAPTER X. SEGRE SETS

CHAPTER XI. NONDEGENERACY CONDITIONS FOR MANIFOLDS

CHAPTER XII. HOLOMORPHIC MAPPINGS OF SUBMANIFOLDS

CHAPTER XIII. MAPPINGS OF REAL-ALGEBRAIC SUBVARIETIES

REFERENCES

INDEX

Notes:

"A Princeton University Press E-Book"--Cover.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400883967

1400883962

OCLC:

950698793