Computational Approach to Riemann Surfaces
This volume offers a well-structured overview of existent computational approaches to Riemann surfaces and those currently in development. The authors of the contributions represent the groups providing publically available numerical codes in this field.
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2013
Alexander I. Bobenko · Christian Klein Editors
Computational Approach to Riemann Surfaces
ABC
Editors
Alexander I. Bobenko
Christian Klein
Institut f¨ ur Mathematik Technische Universit¨ at Berlin Strasse des 17. Juni 136 10623 Berlin Germany [email protected]
Institut de Math´ematiques de Bourgogne Universit´e de Bourgogne 9 avenue Alain Savary 21078 Dijon Cedex France [email protected]
For Author addresses please see List of Contributors on page XI
ISBN: 978-3-642-17412-4 e-ISBN: 978-3-642-17413-1 DOI: 10.1007/978-3-642-17413-1 Springer Heidelberg Dordrecht London New York Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2011920817 Mathematics Subject Classification (2011): 14-XX; 30-XX; 65-XX c Springer-Verlag Berlin Heidelberg 2011 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: deblik Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Riemann surfaces appear in many branches of mathematics and physics, e.g. in differential and algebraic geometry and the theory of moduli spaces, in topological field theories, quantum chaos and integrable systems. The practical use of Riemann surface theory has been limited for a long time by the absence of efficient computational approaches. In recent years considerable progress has been achieved in the numerical treatment of Riemann surfaces which stimulated further research in the subject and led to new applications. The existing computational approaches follow from the various definitions of Riemann surfaces: via non-singular algebraic curves, as quotients under the action of Fuchsian or Schottky groups, or via polyhedral surfaces. It is the purpose of the present volume to give a coherent presentation of the existing or currently being developed computational approaches to Riemann surfaces. The authors of the contributions are representants from the groups providing publically available numerical codes in this field. Thus this volume illustrates which software tools are available and how they can be used in practice. In addition examples for solutions to partial differential equations and in surf
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