Geometry and Spectra of Compact Riemann Surfaces
This classic monograph is a self-contained introduction to the geometry of Riemann surfaces of constant curvature –1 and their length and eigenvalue spectra. It focuses on two subjects: the geometric theory of compact Riemann surfaces of genus greater tha
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Geometry and Spectra of Compact Riemann Surfaces
Peter Buser
Reprint of the 1992 Edition
Peter Buser Département de Mathématiques Ecole Polytechnique Fédérale de Lausanne CH-1015 Lausanne-Ecublens Switzerland [email protected]
Originally published as Volume 106 in the series Progress in Mathematics
e-ISBN 978-0-8176-4992-0 ISBN 978-0-8176-4991-3 DOI 10.1007/978-0-8176-4992-0 Springer New York Dordrecht Heidelberg London Mathematics Subject Classification (2010): 32G15, 53A35, 58C40, 58J53, 11F72, 30F35
© Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper www.birkhauser-science.com
Peter Buser
Geometry and Spectra of Compact Riemann Surfaces with 135 illustrations
Birkhauser Boston • Basel • Berlin
Peter Buser D6partement de Math6matiques Ecole Polytechnique F6d6rale de Lausanne CH-1015 Lausanne-Ecublens Switzerland Library of Congress Cataloging-in-Publication Data Buser, Peter, 1946Geometry and spectra of compact Riemann surfaces / Peter Buser. p. cm. — (Progress in mathematics ; v. 106) Includes bibliographical and references and index. ISBN 0-8176-3406-1 (acid free) 1. Riemann surfaces. I. Title. II. Series: Progress in mathematics (Boston, Mass.) ; vol. 106. QA333.B87 1992 92-23803 515' .223~dc20 CIP
Printed on acid-free paper © Birkhauser Boston 1992 Copyright is not claimed for works of U.S. Government employees. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photo copying, recording, or otherwise, without prior permission of the copyright owner. Permission to photocopy for internal or personal use of specific clients is granted by Birkhauser Boston for libraries and other users registered with the Copyright Clearance Center (CCC), provided that the base fee of $5.00 per copy, plus $0.20 per page is paid directly to CCC, 21 Congress Street, Salem, MA 01970, U.S.A. Special requests should be addressed directly to Birkhauser Boston, 675 Massachusetts Avenue, Cambridge, MA 02139, U.S.A. ISBN 0-8176-3406-1 ISBN 3-7643-3406-1 Camera-ready copy prepared by the Authors in TeX. Printed and bound by Quinn-Woodbine, Woodbine, NJ. Printed in the U.S.A. 987654321
To Barbara Caroline Patrick Regula
Preface This book deals with two subjects. The first su
