Minimal Surfaces
Minimal Surfaces is the first volume of a three volume treatise on minimal surfaces (Grundlehren Nr. 339-341). Each volume can be read and studied independently of the others. The central theme is boundary value problems for minimal surfaces. The treatise
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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
339
The Costa surface. Courtesy of D. Hoffman
For further volumes: http://www.springer.com/series/138
Ulrich Dierkes Stefan Hildebrandt Friedrich Sauvigny
Minimal Surfaces With assistance and contributions by A. Küster and R. Jakob
Revised and enlarged 2nd edition With 139 Figures and 9 Color Plates
Ulrich Dierkes Faculty of Mathematics University of Duisburg-Essen Campus Duisburg Forsthausweg 2 47057 Duisburg Germany [email protected]
Stefan Hildebrandt Mathematical Institute University of Bonn Endenicher Allee 60 53115 Bonn Germany
Friedrich Sauvigny Mathematical Institute Brandenburgian Technical University Konrad-Wachsmann-Allee 1 03044 Cottbus Germany [email protected] With contributions by Ruben Jakob Faculty of Mathematics University of Duisburg-Essen Campus Duisburg Forsthausweg 2 47048 Duisburg Germany [email protected]
Albrecht Küster Walter-Flex-Str. 19 47809 Krefeld Germany
This volume is the first part of a treatise on Minimal Surfaces in the series Grundlehren der mathematischen Wissenschaften. Part Two is Vol. 340 ISBN 978-3-642-11699-5, 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 ISBN 978-3-642-11697-1 e-ISBN 978-3-642-11698-8 DOI 10.1007/978-3-642-11698-8 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010930922 Mathematics Subject Classification (2010): 49Q05, 53A05, 53A07, 53B20, 35J20, 35J4 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 first 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 pr
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