Real Submanifolds in Complex Space and Their Mappings (PMS–47) (Princeton Mathematical Series, 47) - Hardcover

Baouendi, M. Salah; Ebenfelt, Peter; Rothschild, Linda Preiss

Hardcover

ISBN 10: 0691004986 ISBN 13: 9780691004983

Publisher: Princeton University Press, 1999

Synopsis

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.

About this title

About the Author

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.

Edition details

• Publisher: Princeton University Press
• Publication date: 1999
• Language: English
• ISBN 10: 0691004986
• ISBN 13: 9780691004983
• Binding: Hardcover
• Number of pages: 416