Regularity of Minimal Surfaces
Regularity of Minimal Surfaces begins with a survey of minimal surfaces with free boundaries. Following this, the basic results concerning the boundary behaviour of minimal surfaces and H-surfaces with fixed or free boundaries are studied. In particular,
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Series editors M. Berger P. de la Harpe F. Hirzebruch N.J. Hitchin L. Hörmander M. Kashiwara A. Kupiainen G. Lebeau F.-H. Lin B.C. Ngô M. Ratner D. Serre Ya.G. Sinai N.J.A. Sloane A.M. Vershik M. Waldschmidt Editor-in-Chief A. Chenciner J. Coates S.R.S. Varadhan
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Half of an analog to Costa’s surface which is stationary in a configuration consisting of four nearly semicircular arcs and a plane. Courtesy of K. Polthier
For further volumes: http://www.springer.com/series/138
Ulrich Dierkes Stefan Hildebrandt Anthony J. Tromba
Regularity of Minimal Surfaces With assistance and contributions by A. Küster
Revised and enlarged 2nd edition With 62 Figures and 4 Color Plates
Ulrich Dierkes Fakultät für Mathematik Universität Duisburg-Essen Campus Duisburg Forsthausweg 2 47057 Duisburg Germany [email protected]
Stefan Hildebrandt Mathematical Institute University of Bonn Endenicher Allee 60 53115 Bonn Germany
Anthony J. Tromba Department of Mathematics University of California at Santa Cruz Baskin 621B CA 95064 Santa Cruz USA [email protected]
With contributions by Albrecht Küster Walter-Flex-Str. 19 47809 Krefeld Germany This volume is the second part of a treatise on Minimal Surfaces in the series Grundlehren der mathematischen Wissenschaften. Part One is Vol. 339 ISBN 978-3-642-11697-1, Part Three is Vol. 341 ISBN 9783-642-11705-3. A 1st edition of the treatise appeared as Vols. 295 and 296 of the same series.
ISSN 0072-7830 e-ISBN 978-3-642-11700-8 ISBN 978-3-642-11699-5 DOI 10.1007/978-3-642-11700-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010930923 Mathematics Subject Classification (2010): 49Q05, 53A05, 53A07, 53B20, 35J20, 35J47, 35J50, 35J75, 49Q20, 30C20 c Springer-Verlag Berlin Heidelberg 1992, 2010 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: VTEX, Vilnius Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
This book is the second volume of a treatise on minimal surfaces consisting of altogether three volumes which can be read and studied independently of each other. The central theme is boundary value problems for minimal surfaces such as Plateau’s problem. The present treatise fo
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