Compact Riemann Surfaces An Introduction to Contemporary Mathematics
Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it dev
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Springer-Verlag Berlin Heidelberg GmbH
Jiirgen Jost
Compact Riemann Surfaces An Introduction to Contemporary Mathematics
Second Edition
Springer
Jiirgen Jost Max Planck Institute for Mathematics in the Sciences Inselstr.22-26 04103 Leipzig Germany
Library of Congress Cataloging-in Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Jost, Jtirgen: Compact Riemann surfaces: an introduction to contemporary mathematics 1 Jilrgen Jost. - 2. ed.. Einheitssacht.: Riemannsche FIăchen ISBN 978-3-540-43299-9 DOI 10.1007/978-3-662-04745-3
ISBN 978-3-662-04745-3 (eBook)
Mathematics Subject Classification (2000): 30FlO, 30F45, 30F60, 58E20, 14H55
This work is subject to copyright. AII rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of iIIustrations. recitation. broadcasting, reproduction on microfilms 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-Verlag. Violations are Iiable for prosecution under the German Copyright Law.
http://www.springer.de © Springer-Verlag Berlin Heidelberg 2002 Driginally published by Springer-Verlag Berlin Heidelberg New York in 2002
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. Typesetting: Camera-ready copy produced by the author using a Springer T EX macro package Cover design: design 6- production GmbH, Heidelberg Printed on acid-free paper
SPIN: 10866725
41/3142/db - 5 4 3 2 1 o
Dedicated to my parents
Preface
The present book started from a set of lecture notes for a course taught to students at an intermediate level in the German system (roughly corresponding to the beginning graduate student level in the US) in the winter term 86/87 in Bochum. The original manuscript has been thoroughly reworked several times although its essential aim has not been changed. Traditionally, many graduate courses in mathematics, and in particular those on Riemann surface theory, develop their subject in a most systematic, coherent, and elegant manner from a single point of view and perspective with great methodological purity. My aim was instead to exhibit the connections of Riemann surfaces with other areas of mathematics, in particular (twodimensional) differential geometry, algebraic topology, algebraic geometry, the calculus of variations and (linear and nonlinear) elliptic partial differential equations. I consider Riemann surfaces as an ideal meeting ground for analysis, geometry, and algebra and as ideally suited for displaying the unity of mathematics. Therefore, they are perfect for introducing intermediate students to advanced mathematic
