Metric Structures for Riemannian and Non-Riemannian Spaces
Metric theory has undergone a dramatic phase transition in the last decades when its focus moved from the foundations of real analysis to Riemannian geometry and algebraic topology, to the theory of infinite groups and probability theory. The new wave beg
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Metric Structures for Riemannian and Non-Riemannian Spaces
Misha Gromov With Appendices by M. Katz, P. Pansu, and S. Semmes English translation by Sean Michael Bates
Reprint of the 2001 Edition Birkhauser Boston • Basel • Berlin
Mikhail Gromov Institut des Hautes Etudes Scientifiques Departement de Mathematiques F-91440 Bures-sur-Yvette France
Originally published as volume 152 in the series Progress in Mathematics
Cover design by Alex Gerasev. Mathematics Subject Classification (2000): 01A60, 01A75, 51K99, 53-02, 53C20, 53C23, 53C70, 57N65 Library of Congress Control Number: 2006937425 ISBN-10: 0-8176-4582-9
e-ISBN-10: 0-8176-4583-7
ISBN-13: 978-0-8176-4582-3
e-ISBN-13: 978-0-8176-4583-0
Printed on acid-free paper ©2007 Birkhauser Boston BirUhaUSCr Based on Structures Metriques des Varietes Riemanniennes Edited by J. LaFontaine and P. Pansu All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkhauser Boston, c/o 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. 9 8 7 6 5 4 3 2 1 www.birkhauser.com
(IBT)
Misha Gromov with Appendices by
M. Katz, P. Pansu, and S. Semmes"
Metric Structures for Riemannian and Non-Riemannian Spaces Based on Structures Metriques des Varietes Riemanniennes Edited by J. LaFontaine and P. Pansu English Translation by Sean Michael Bates
Birkhauser Boston • Basel • Berlin
Author Mikhail Gromov Departement de Mathematiques Institut des Hautes Etudes Scientifiques Bures-sur-Yvette, France
Translator (English edition) Sean Michael Bates Department of Mathematics Columbia University New York, NY 10027, USA
Editors (French Edition) Jacques LaFontaine Departement des Sciences Mathematiques Universite de Montpellier 2, Place E. Bataillon, 34095 Montpellier Cedex 5, France
Pierre Pansu Departement de Mathematiques Universite de Paris-Sud 91405 Orsay Cedex, France
Library of Congress Cataloging-in-Publication Data Gromov, Mikhail [Structures metriques des varietes riemanniennes. English] Metric structures for Riemannian and non-Riemannian spaces / Mikhail Gromov ; translated by Sean Michael Bates, p. cm. - (Progress in mathematics ; v. 152) Includes bibliographical references and index. ISBN 0-8176-3898-9 (acid-free paper) 1. Riemannian manifolds. I. Title. II. Series: Progress in mathematics (Boston, Mass.) ; vol. 152. QA629.G8313 1998 97-24633 516.373-DC21 CIP AMS Subject Classifications: 53B21, 53C20, 53C21, 53C23, 58D17, 54E35, 51H20, 51H25, 54E35, 28A78 Print
