Riemannian Geometry and Geometric Analysis
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 cond
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Springer-Verlag Berlin Heidelberg GmbH
Jiirgen Jost
Riemannian
Geometry
and Geometric Analysis Third Edition
Springer
Jiirgen Jost Max Planck Institute for Mathematics in the Sciences Inselstr. 22-26 04103 Leipzig Germany
Library of Congress Cataloging-in Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Jost, Jiirgen: Riemannian geometry and geometric analysis I Jiirgen Jost. (Universitext) ISBN 978-3-540-42627-1 ISBN 978-3-662-04672-2 (eBook) DOl 10.1007/978-3-662-04672-2
Mathematics Subject Classification (2000): 53B21, 53L20, 32C17, 35160, 49-XX, 58E20, 57R15
ISBN 978-3-540-42627-1
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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 extremal problems naturally arising in geometry and for investigating and characterizing their solutions. It turns out that the two fields complement each other very well; geometric analysis offers tools for solving difficult problems in geometry, and Riemannian geometry stimulates progress in geometric analysis by setting ambitious goals. It is the aim of this book to be a systematic and comprehensive introduction to Riemannian geometry and a representative introduction to the methods of geometric analysis. It attempts a synthesis of geometric and analytic methods in the study of Riemannian manifolds. The present work is the third edition of my textbook on Riema
