Some Nonlinear Problems in Riemannian Geometry
During the last few years, the field of nonlinear problems has undergone great development.This book, the core of which is the content of the author's earlier book (Springer-Verlag 1983), updated and extended in each chapter, and augmented by several comp
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Springer-Verlag Berlin Heidelberg GmbH
Thierry Aubin
Some Nonlinear Problems •
In
Riemannian Geometry
Springer
Thierry Aubin University of Paris VI Mathematiques 4, Place Jussieu, Boite 172 F-7S2S2 Paris France
llbrary of Congress Cataloglng-In-Publlcatlon Data Aubin. Thierry. Some nonlinear problens in Rlemannlan geometry I Thlerry Aubln. en. -- (Springer monographs in mathenatics) p. Ineludes blbllographlcal references and Index. ISBN 978-3-642-08236-8 ISBN 978-3-662-13006-3 (eBook) DOI 10.1007/978-3-662-13006-3
1. Geometry. Rtemanntan. II. Sertes.
2. Nonltnear theortes.
OA649.A833 1998 516.3·73--de21
1. Tttle. 98-4150
CIP
Mathematics Subject Classification (1991); 35,53,58
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© Springer-Verlag Berlin Heidelberg 1998 Originally published by Springer-Verlag Berlin Heidelberg New York in 1998 The use of general descriptive names, registered names, trademarks etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by A. Leinz, Karlsruhe SPIN 10518869 41/3143-543210 - Printed an acid-freepaper
Preface
This book is the union of two books: the new edition of the former one "Nonlinear Analysis on Manifolds. Monge-Ampere Equations" (Grundlehren 252 Springer 1982) mixed with a new one where one finds, among other things, up-to-date results on the problems studied in the earlier one, and new methods for solving nonlinear elliptic problems. We will give below successively the prefaces of the two books, and at the end of the volume, the two bibliographies (the references * are new). A very interesting area of nonlinear partial differential equations lies in the study of special equations arising in Geometry and Physics. This book deals with some important geometric problems that are of interest to many mathematicians and scientists but have only recently been partially solved. Each problem is explained, up-to-date results are given and proofs are presented. Thus the reader is given access, for each specific problem, to its present status of solution as well as to most up-to-date methods for approaching it. The book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing up technique, geometric and topological methods. My
