M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild

Real Submanifolds in Complex Space and Their Mappings (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Manchester University Press
• Erscheinungstermin: 2. Juni 2016
• Englisch
• ISBN-13: 9781400883967
• Artikelnr.: 45117109

Autorenporträt

M. Salah Baouendi and Linda Preiss Rothschild are Professors of Mathematics at the University of California, San Diego. Peter Ebenfelt is Associate Professor of Mathematics at the Royal Institute of Technology, Stockholm, Sweden.

Inhaltsangabe

Preface
Ch. I
Hypersurfaces and Generic Submanifolds in C[superscript N]<
3
Ch. II
Abstract and Embedded CR Structures
35
Ch. III
Vector Fields: Commutators, Orbits, and Homogeneity
62
Ch. IV
Coordinates for Generic Submanifolds
94
Ch. V
Rings of Power Series and Polynomial Equations
119
Ch. VI
Geometry of Analytic Discs
156
Ch. VII
Boundary Values of Holomorphic Functions in Wedges
184
Ch. VIII
Holomorphic Extension of CR Functions
205
Ch. IX
Holomorphic Extension of Mappings of Hypersurfaces
241
Ch. X
Segre Sets
281
Ch. XI
Nondegeneracy Conditions for Manifolds
315
Ch. XII
Holomorphic Mappings of Submanifolds
349
Ch. XIII
Mappings of Real-algebraic Subvarieties
379
References
390
Index
401