Holomorphic Curves and Global Questions in Contact Geometry
This book explains the foundations of holomorphic curve theory in contact geometry. By using a particular geometric problem as a starting point the authors guide the reader into the subject. As such it ideally serves as preparation and as entry point for
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Casim Abbas Helmut Hofer
Holomorphic Curves and Global Questions in Contact Geometry
Birkhäuser Advanced Texts Basler Lehrbücher
Series editors Steven G. Krantz, Washington University, St. Louis, USA Shrawan Kumar, University of North Carolina at Chapel Hill, Chapel Hill, USA Jan Nekováˇr, Université Pierre et Marie Curie, Paris, France
More information about this series at http://www.springer.com/series/4842
Casim Abbas • Helmut Hofer
Holomorphic Curves and Global Questions in Contact Geometry
Casim Abbas Michigan State University East Lansing, MI, USA
Helmut Hofer Institute for Advanced Study Princeton, NJ, USA
ISSN 1019-6242 ISSN 2296-4894 (electronic) Birkhäuser Advanced Texts Basler Lehrbücher ISBN 978-3-030-11802-0 ISBN 978-3-030-11803-7 (eBook) https://doi.org/10.1007/978-3-030-11803-7 Library of Congress Control Number: 2019930036 Mathematics Subject Classification (2010): 58-xx, 37-xx, 32-xx © Springer Nature Switzerland AG 2019 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 book is published under the imprint Birkhäuser, www.birkhauser-science.com by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Dedicated to the Memory of Andreas Floer and Kris Wysocki
Andreas Floer Author: George M. Bergman. Source: Archives of the Mathematisches Forschungsinstitut Oberwolfach
Kris Wysocki Author: Jürgen Pöschel. Source: Archives of the Mathematisches Forschungsinstitut Oberwolfach
Introduction
Historical Background In 1976, in his paper [91], Jürgen Moser writes about the classical action principle the following: “However, this variational principle is very degenerate, for example even the Legendre condition is violated, and is certainly not suitable for an existence proof.” If this statement would be true, modern symplectic geometry would not exist. In essen
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