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

• Superior document: Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
• VerfasserIn: Baouendi, M. Salah,; Ebenfelt, Peter,; Rothschild, Linda Preiss,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1999
• Year of Publication: 2016
• Language: English
• Series: Princeton Mathematical Series
• Physical Description: 1 online resource (416 p.)

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.

Table of 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