Expository Lecture s from th e CBMS Regional Conferenc e held a t th e Polytechni c Institut e o f Ne w York January 6-10 , 198 4 Research supporte d i n par t b y Nationa l Scienc e Foundatio n Gran t MC S 82-01140. 1980 Mathematics Subject Classifications. Primar y 35Jxx , 53Cxx . Library o f Congres s Cataloging in Publication Dat a Kazdan, Jerry L. , 1937 - Prescribing th e curvatur e o f a Riemannian manifold . (Regional conferenc e serie s in mathematics no. 57 ) "Expository lecture s fro m th e CBM S regional conferenc e hel d a t th e Polytechni c Institute o f Ne w York, January 6-10 , 1984" Bibliography: p . 1. Riemannia n manifolds . 2 . Curvature. I . Conference Boar d of th e Mathematica l Sciences. II . Title. III . Series. QA1.R33 no . 5 7 [QA649 ] 510 s [516.3'62 ] 84-2827 4 ISBN 0-8218-0707-2 (alk . paper ) Copying an d reprinting. Individua l reader s of this publication , an d nonprofit librarie s actin g for them , are permitted t o make fair us e of the material, suc h as to copy an article for use in teaching or research. Permissio n is granted to quote brief passages from this publication in reviews, provided the customary acknowledgemen t o f the source is given. Republication, systemati c copying , or multiple production o f any materia l i n this publication (in- cluding abstracts) i s permitted onl y unde r licens e from th e American Mathematica l Society . Request s for suc h permissio n shoul d b e addressed t o the Executive Director , America n Mathematica l Society , P.O. Box 6248, Providence, Rhode Island 02940. The owner consents to copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided tha t a fee of $1.00 plus $.2 5 per page fo r each cop y b e paid directl y t o the Copyright Clearance Center , Inc. , 21 Congress Street , Salem , Massachusett s 01970 . Whe n payin g this fee please use the code 0160-7642/85 to refer t o this publication . Thi s consent doe s not extend t o other kind s of copying, suc h a s copying fo r general distribution , fo r advertising o r promotion purposes , fo r creating new collective works, or for resale. Copyright © 1985 by the American Mathematical Society Reprinted with corrections 1987 Printed in the United States of America All rights reserved except those granted to the United States Government The paper used in this book is acid-free and faUs within the guidelines established to ensure permanence and durability. @
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