
M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild

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Author: M. Salah Baouendi,Peter Ebenfelt,Linda Preiss Rothschild
Publisher: Princeton University Press
ISBN: 1400883962
Category: Mathematics
Page: 416
View: 7259
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 CauchyRiemann equations on real submanifolds. They present the main results in this area with a novel and selfcontained 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, CauchyRiemann vector fields and their orbits play a central role and are presented in a setting that is both general and elementary.