Real Submanifolds in Complex Space and Their Mappings (häftad)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
416
Utgivningsdatum
1999-01-01
Förlag
Princeton University Press
Originalspråk
English
Medarbetare
Rothschild, Linda Preiss
Illustrationer
black & white illustrations
Dimensioner
242 x 165 x 33 mm
Vikt
745 g
Antal komponenter
1
Komponenter
55:B&W 6.14 x 9.21in or 234 x 156mm (Royal 8vo) Gray Cloth on White
ISBN
9780691004983

Real Submanifolds in Complex Space and Their Mappings

av M Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild
Inbunden,  Engelska, 1999-01-01
1542
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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.
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Övrig information

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.

Innehållsförteckning

PrefaceCh. IHypersurfaces and Generic Submanifolds in C[superscript N]3Ch. IIAbstract and Embedded CR Structures35Ch. IIIVector Fields: Commutators, Orbits, and Homogeneity62Ch. IVCoordinates for Generic Submanifolds94Ch. VRings of Power Series and Polynomial Equations119Ch. VIGeometry of Analytic Discs156Ch. VIIBoundary Values of Holomorphic Functions in Wedges184Ch. VIIIHolomorphic Extension of CR Functions205Ch. IXHolomorphic Extension of Mappings of Hypersurfaces241Ch. XSegre Sets281Ch. XINondegeneracy Conditions for Manifolds315Ch. XIIHolomorphic Mappings of Submanifolds349Ch. XIIIMappings of Real-algebraic Subvarieties379References390Index401

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