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Real Submanifolds in Complex Space and Their Mappings (PMS-47) : Princeton Mathematical Series - M. Salah Baouendi

Real Submanifolds in Complex Space and Their Mappings (PMS-47)

Princeton Mathematical Series

Hardcover Published: 17th January 1999
ISBN: 9780691004983
Number Of Pages: 416

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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.

Hypersurfaces and Generic Submanifolds in C[superscript N]p. 3
Abstract and Embedded CR Structuresp. 35
Vector Fields: Commutators, Orbits, and Homogeneityp. 62
Coordinates for Generic Submanifoldsp. 94
Rings of Power Series and Polynomial Equationsp. 119
Geometry of Analytic Discsp. 156
Boundary Values of Holomorphic Functions in Wedgesp. 184
Holomorphic Extension of CR Functionsp. 205
Holomorphic Extension of Mappings of Hypersurfacesp. 241
Segre Setsp. 281
Nondegeneracy Conditions for Manifoldsp. 315
Holomorphic Mappings of Submanifoldsp. 349
Mappings of Real-algebraic Subvarietiesp. 379
Referencesp. 390
Indexp. 401
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691004983
ISBN-10: 0691004986
Series: Princeton Mathematical Series
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 416
Published: 17th January 1999
Country of Publication: US
Dimensions (cm): 24.16 x 16.46  x 3.25
Weight (kg): 0.74

Earn 332 Qantas Points
on this Book