Riemannian Geometry and Geometric Analysis
This established reference work continues to lead its readers to some of the hottest topics of contemporary mathematical research. The previous edition already introduced and explained the ideas of the parabolic methods that had found a spectacular succes
- PDF / 6,169,177 Bytes
- 616 Pages / 439.37 x 666.142 pts Page_size
- 53 Downloads / 249 Views
Universitext Series Editors: Sheldon Axler San Francisco State University Vincenzo Capasso Università degli Studi di Milano Carles Casacuberta Universitat de Barcelona Angus J. MacIntyre Queen Mary, University of London Kenneth Ribet University of California, Berkeley Claude Sabbah CNRS, École Polytechnique Endre Süli University of Oxford Wojbor A. Woyczynski Case Western Reserve University
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext.
For further volumes: www.springer.com/series/223
Jürgen Jost
Riemannian Geometry and Geometric Analysis
123
Jürgen Jost Max Planck Institute for Mathematics in the Sciences Inselstr. 22 04103 Leipzig Germany [email protected]
ISBN 978-3-642-21297-0 e-ISBN 978-3-642-21298-7 DOI 10.1007/978-3-642-21298-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011932682 Mathematics Subject Classification (2010): 53B21, 53L20, 32C17, 35I60, 49-XX, 58E20, 57R15 © Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Shing-Tung Yau, for so many discussions about mathematics and Chinese culture
•
Preface
Riemannian geometry is characterized, and research is oriented towards and shaped by concepts (geodesics, connections, curvature, . . . ) and objectives, in particular to understand certain classes of (compact) Riemannian manifolds defined by curvature conditions (constant or positive or negative curvature, . . . ). By way of contrast, geometric analysis is a perhaps somewhat less systematic collection of techniques, for solving extrem
Data Loading...
