Constant Mean Curvature Surfaces with Boundary
The study of surfaces with constant mean curvature (CMC) is one of the main topics in classical differential geometry. Moreover, CMC surfaces are important mathematical models for the physics of interfaces in the absence of gravity, where they separate tw
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Rafael López
Constant Mean Curvature Surfaces with Boundary
Rafael López Department of Geometry and Topology University of Granada Granada, Spain
ISSN 1439-7382 ISSN 2196-9922 (electronic) Springer Monographs in Mathematics ISBN 978-3-642-39625-0 ISBN 978-3-642-39626-7 (eBook) DOI 10.1007/978-3-642-39626-7 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013948448 Mathematics Subject Classification (2010): 53, 53A, 53A10, 53C42, 35J, 35J60 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Elia and Irene, my daughters
Preface
Surfaces of constant mean curvature (cmc surfaces) play an important role in classical differential geometry because they are the local solutions of one of the oldest problems in geometry, namely, the isoperimetric problem: find those surfaces of least area enclosing a prescribed volume. These surfaces are of great interest not only for mathematicians, but also for physicists and engineers since they provide mathematical models in contexts where a physical system seeks a state of least energy. A number of texts are available which deal with this type of surface in more or less depth. The classical boo
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