Harmonic Maps, Conservation Laws And Moving Frames

E-Book Overview

This accessible introduction to harmonic map theory and its analytical aspects, covers recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.

E-Book Content

CAMBRIDGE TRACTS IN MATHEMATICS General Editors B. BOLLOBAS, W. FULTON, A. KATOK, F. KIRWAN, P. SARNAK 150 Harmonic maps, conservation laws and moving frames Second edition This page intentionally left blank Harmonic maps, conservation laws and moving frames Second edition Fr´ed´eric H´elein Ecole Normale Sup´ erieure de Cachan PUBLISHED BY CAMBRIDGE UNIVERSITY PRESS (VIRTUAL PUBLISHING) FOR AND ON BEHALF OF THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge CB2 IRP 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia http://www.cambridge.org © Frédéric Hélein 2002 This edition © Frédéric Hélein 2003 First published in printed format 2002 Second edition 2002 A catalogue record for the original printed book is available from the British Library and from the Library of Congress Original ISBN 0 521 81160 0 hardback ISBN 0 511 01660 3 virtual (netLibrary Edition) <
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