Real Submanifolds in Complex Space and Their Mappings

PMS-47

M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild

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English

Princeton University Press
30 March 1999

Complex analysis, complex variables; Differential calculus & equations; Differential & Riemannian geometry; Analytic geometry; Algebraic geometry

Series: Princeton Mathematical Series

Presenting the main developments of the past two decades in the study of real submanifolds in complex space, this book covers the techniques in this area which borrow from real and complex analysis and partial differential equations, as well as from differential, algebraic and analytical geometry. One of the more important topics covered here is the holomorphic extension of functions and mappings that satisfy the tangential Cauchy-Riemann equations on rweal submanifolds, presenting the main results in this area. It also devotes attention to the study of holomorphic mappings between real submanifolds, and proves finite determination of such mappings by their jets under some optimal assumptions. Throughout the book, Cauchy-Riemann vector fields and their orbits play a central role.

By: M. Salah Baouendi, Peter Ebenfelt, Linda Preiss Rothschild
Imprint: Princeton University Press
Country of Publication: United States
Volume: v. 47
Dimensions: Height: 235mm, Width: 152mm, Spine: 33mm
Weight: 709g
ISBN: 9780691004983
ISBN 10: 0691004986
Series: Princeton Mathematical Series
Pages: 416
Publication Date: 30 March 1999
Audience: Professional and scholarly , College/higher education , Undergraduate , Primary
Format: Hardback
Publisher's Status: Active

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

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.