A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation
This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation. Such solutions (if real-valued) correspond to certain constant mean curvature surfaces in Eucli
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Sebastian Klein
A Spectral Theory for Simply Periodic Solutions of the SinhGordon Equation
Lecture Notes in Mathematics Editors-in-Chief: Jean-Michel Morel, Cachan Bernard Teissier, Paris Advisory Board: Michel Brion, Grenoble Camillo De Lellis, Princeton Alessio Figalli, Zurich Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gábor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, New York Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Sebastian Klein
A Spectral Theory for Simply Periodic Solutions of the Sinh-Gordon Equation
123
Sebastian Klein School of Business Informatics & Mathematics University of Mannheim Mannheim, Germany
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-030-01275-5 ISBN 978-3-030-01276-2 (eBook) https://doi.org/10.1007/978-3-030-01276-2 Library of Congress Control Number: 2018961014 Mathematics Subject Classification (2010): Primary: 37K10, 53A10, 58E12; Secondary: 35P05, 35R30, 37K15, 37K25, 40A05, 40A10, 40A20, 42B05, 46B45, 46C05, 46E15, 46E35 © Springer Nature Switzerland AG 2018 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book on a spectral theory for simply periodic solutions of the sinh-Gordon equation is the result of my habilitation project at the University of Mannheim. I would like to express my sincerest gratitude to Professor Martin U. Schmidt, who has advised me during the creation of this work. His steady support and help has been invaluable to me. I have learned a lot from him. I would also like to thank Professor C. Hertling for the introductory seminary on algebraic geometry and for further advice, Dr. Markus
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