EDITED BY PROVIDENCE,RHODEISLAND USA ISSN

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1 EDITED BY William Adams J. Marshall Ash Maurice Ausler Andreas R. Blass Thomas H. Brylawski Dennis Burke Frederick R. Cohen William J. Davis, Managing Editor Clifford J. Earle, Jr. Palle E. T. Jorgensen Barbara L. Keyfitz R. Daniel Mauldin Kenneth R. Meyer Paul S. Muhly Andrew Odlyzko George C. Papanicolaou Louis J. Ratliff, Jr. Jonathan M. Rosenberg William D. Sudderth James E. West Warren J. Wong PROVIDENCE,RHODEISLAND USA ISSN

2 Proceedings of the American Mathematical Society This journal is devoted entirely to research in pure applied mathematics. Editorial Policy To be published in the Proceedings, a paper must be correct, new, nontrivial significant. Further, it must be well written of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Proceedings Editors shall solicit, encourage publication of, worthy papers of length not exceeding 15 typed pages. Very short notes not to exceed two printed pages are also accepted, appear under the heading Shorter notes. Items deemed suitable include an elegant new proof of an important well-known theorem, an illluminating example or counterexample, or a new viewpoint on familiar results. New results, if of a brief striking character, might also be acceptable, though in general a paper which is merely very short will not be suitable for the Shorter notes department. On January 23, 1979, the Council of the American Mathematical Society abolished blind refereeing as a policy for the Proceedings, but decided that any author who so requests who provides a blind copy of a manuscript will have the manuscript refereed blind. Two copies of a manuscript should be submitted. If blind refereeing is intended, one should be complete one blind, then the latter will be sent to the referee without disclosure of the author's name or institution. SUBSCRIPTION INFORMATION. PROCEEDINGS OF THE AMERICAN MATHEMATI- CAL SOCIETY is published monthly. Subscription prices for Volumes (1989) are $413 list; $330 institutional member; $248 individual member. A late charge of 10% of the subscription price will be imposed upon orders received from nonmembers after January 1 of the subscription year. Subscribers outside the United States India must pay a postage surcharge of $25: subscribers in India must pay a postage surcharge of $38. Expedited delivery to destinations in North America $30; elsewhere $40. Combination paper microfiche subscription prices are $549 list; $439 institutional member. Microfiche of each issue will be mailed the fastest way possible before the camera copy is sent to the printer. Microfilm subscriptions may be purchased from University Microfilms International, 300 North Zeeb Road, Ann Arbor, Michigan BACK NUMBER INFORMATION. Back number prices per volume are for Volumes 1-89, $113 list, $90 institutional; for Volumes 90-92, $129 list; $103 institutional member; for Volumes 93-95, $173 list; $138 institutional member; for Volumes 96-98, $191 list; $153 institutional members; for Volumes , $202 list; $162 institutional member. Subscriptions orders for publications of the American Mathematical Society should be addressed to American Mathematical Society, P. O. Box 1571, Annex Station, Providence, R. I All orders must be accompanied by payment. Other correspondence should be addressed to P. O. Box 6248, Providence, R. I PROCEEDINGS of the American Mathematical Society is published monthly by the American Mathematical Society at 201 Charles Street, Providence, R. I Second-class postage is paid at Providence, Rhode Isl. Postmaster: Send address changes to PROCEEDINGS, American Mathematical Society, P. O. Box 6248, Providence, R. I Copyright 1989 American Mathematical Society. All rights reserved. Printed in the United States of America Information on Copying Reprinting can be found at the back of this journal. The paper used in this journal is acid-free falls within the guidelines established to ensure permanence This publication was typeset using Aj^S-T^X., the American Mathematical Society's TgX macro system.

3 Manuscript Information 1. Articles submitted for publication should be typewritten, double spaced, no more than 15 (85" x 11") pages long. The Manual for Authors, available from the Society, should be consulted for symbols style conventions. Authors should take the greatest possible care in preparing the original manuscript. H drawn symbols are satisfactory, if clearly done; directions to the printer should be included where necessary on a separate sheet. Authors must keep complete copies of their manuscripts, editors will acknowledge receipt. To encourage the submission of manuscripts in electronic form using T^X the Ajvß-TpX macro package, the Executive Committee of the Council has adopted a policy that allows for accelerating the publication date of such manuscripts by as much as 20 weeks, which is approximately equal to the time normally needed by the Society for copyediting, typesetting, proofreading an average manuscript. 2. The first page should consist of a descriptive title, followed by an abstract which summarizes the article in language suitable for workers in the general field (algebra, analysis, etc.). The descriptive title should be short, but informative; useless or vague phrases such as "some remarks about" or "concerning" should be avoided. The abstract should be at least one complete sentence, at most 150 words. Included with the footnotes to the paper, but placed before the first footnote, there should be first the 1980 Mathematics Subject Classification ( 1985 Revision) representing the primary secondary subjects of the article. This may be followed by a list of key words phrases describing the subject matter of the article taken from it. A list of the numbers may be found in the annual subject index of Mathematical Reviews, published with the December issue starting in A Copyright Transfer Agreement is required before a paper will be published in the Proceedings. A copy of the form is sent with the acknowledgement of receipt of manuscript from the Providence office of the Society. Authors are urged to return the forms immediately to prevent delays in processing publishing of the manuscript. OFFPRINTS AND ADDRESS CHANGES. Any inquiries concerning a paper which has been accepted for publication, including information regarding offprints or changes of address for mailing proof, should be sent directly to the Editorial Department, American Mathematical Society, P.O. Box 6248, Providence, Rhode Isl GALLEY PROOF. When a paper with more than one author has been accepted for publication, only one set of galley proof will be sent. Joint authors should, therefore, indicate on the original manuscript which of them should receive galley proof in the event that the manuscript is accepted for publication. BACKLOG. 150 pages. Papers currently being accepted by the editors will be published in months. COPYING AND REPRINTING. Individual readers of this publication, nonprofit libraries acting for them are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews provided the customary acknowledgement of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Executive Director, American Mathematical Society, P.O. Box 6248, Providence, Rhode Isl The appearance of the code on the first page of an article in this journal indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to Copyright Clearance Center, Inc., 21 Congress Street, Salem, Massachusetts This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotion purposes, for creating new collective works, or for resale.

4 Submission of Manuscript Send papers directly to one of the editors listed under the subject field of the paper. The numbers in parentheses are the first two digits of major classification from the 1980 Mathematics Subject Classification (1985 Revision) describe the fields being hled by the editor. LOGIC AND FOUNDATIONS (03 04) Andreas R. Blass, Department of Mathematics, University of Michigan, Ann Arbor, Michigan COMBINATORICS AND DISCRETE MATHEMATICS (05 15) Thomas H. Brylawski, Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina COMBINATORICS, COMPUTER SCIENCE AND INFORMATION THEORY ( ) Andrew Odlyzko, Room 2C-370, Bell Laboratories, Murray Hill, New Jersey COMMUTATIVE ALGEBRA ( ) Louis J. Ratliff, Jr., Department of Mathematics, University of California, Riverside, California GENERAL ALGEBRA ( ) Maurice Ausler, Department of Mathematics, Breis University, P.O. Box 9110, Waltham, Massachusetts GROUP THEORY (20) Warren J. Wong, Department of Mathematics, University of Notre Dame, Notre Dame, Indiana ALGEBRAIC AND DIFFERENTIAL TOPOLOGY ( ) Frederick R. Cohen, Department of Mathematics, University of Kentucky, Lexington, Kentucky REAL VARIABLES ( ) R. Daniel Mauldin, Department of Mathematics, North Texas State University, Dentón, Texas COMPLEX VARIABLES ( ) Clifford J. Earle Jr., Cornell University, White Hall, Ithaca, New York NUMBER THEORY (11) William Adams, Department of Mathematics, University of Maryl, College Park, MD ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS ( ) Kenneth R. Meyer, Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio PARTIAL DIFFERENTIAL EQUATIONS (35 49) Barbara Lee Keyfitz, Institute for Mathematics Its Applications, University of Minnesota, 514 Vincent Hall, 206 Church Street S. E., Minneapolis, MN GENERAL ANALYSIS ( ) J. Marshall Ash, Department of Mathematics, DePaul University, Chicago, Illinois FUNCTIONAL ANALYSIS AND OPERATOR THEORY (46 47) Palle E. T. Jorgensen, University of Iowa, Iowa City, Iowa FUNCTIONAL ANALYSIS AND CONVEXITY (46 52) William J. Davis, Department of Mathematics, Ohio State University, Columbus, Ohio COMPLEX VARIABLES, FUNCTIONAL ANALYSIS AND OPERATOR THEORY ( ) Paul S. Muhly, Department of Mathematics, University of Iowa, Iowa City, Iowa LIE GROUPS AND GEOMETRY ( ) Jonathan M. Rosenberg, Department of Mathematics, University of Maryl, College Park, Maryl GENERAL TOPOLOGY (54) Dennis Burke, Department of Mathematics, Miami University of Ohio, Oxford, Ohio James E. West, Department of Mathematics, Cornell University, Ithaca, New York PROBABILITY AND CERTAIN OTHER FIELDS (60-94 inclusive) William D. Sudderth, Department of Statistics, University of Minnesota, Minneapolis, Minnesota George C. Papanicolaou, Applied Mathematics Division, New York University-Courant Institute, 251 Mercer Street, New York, New York All other communications should be addressed to the Managing Editor, William J. Davis, at the above address. ABCDEFGHIJ-89

5 CONTENTS Continued from back cover A cusp closing theorem. By Viktor Schroeder. 797 Spheres with locally pinched metrics. By Robert J. Currier. 803 G. TOPOLOGY Highest weight modules for Hermitian symmetric pairs of exceptional type. By Thomas J. Enright Brad Shelton. 807 Strong homology the proper forcing axiom. By Alan Dow, Petr Simon Jerry E. Vaughan. 821 Large groups of symmetries of hlebodies. By A. Miller B. Zimmermann. 829 Stone-Cech remainders which make continuous images normal. By William Fleissner Ronnie Levy. 839 Mosco convergence the Kadec property. By Jonathan M. Borwein Simon Fitzpatrick. 843 Cofinal families of compact subsets of an analytic set. By Howard Becker.' SHORTER NOTE Errata to "Extensions of continuous functions from dense subspaces." By Robert L. Blair 857

6 PROCEEDINGS OF THE AMERICAN MATHEMATICALSOCIETY CONTENTS Vol. 106, No. 3 July 1989 Whole No. 361 A. ALGEBRA AND NUMBER THEORY Surface subgroups of graph groups. Brigitte Servatius By Herman Servatius, Carl Droms 573. On the coherence weak dimension of the rings R(x) R(x). By Sarah Glaz. The conjugacy problem for finite graph products. By K. J. Horadam. When are Rees congruences principal?. By C. M. Reis. The diophantine equation x2 = Aqn + 4qm + 1. By Maohua Le. Characterizations of the conjugacy of Sylow /7-subgroups of CC-groups. By J. Otal J. M. Peña. 605 On the Popov-Pommerening conjecture for groups of type An. By Lin Tan. Algebraic properties of the shift mapping. By Patrick Dehornoy. Classification of finite groups with all elements of prime order. By Marian Deaconescu On the imbedding of a direct product into a zero-dimensional commutative ring. By Robert Gilmer William Heinzer. An identity in the free Lie algebra. By David Wigner. B. ANALYSIS The Cauchy functional equations in distributions. By E. L. Koh. Sturm-Liouville equations with Besicovitch almost-periodicity. By A. Dzurnak A. B. Mingarelli. A weak-type estimate for Fourier-Bessel multipliers. By John Gosselin Krzysztof Stempak. A short proof of the Grigorchuk-Cohen cogrowth theorem. By Ryszard Szwarc. Second order differential equations with rational coefficients. By A. Hinkkanen John Rossi. Composition operators induced by functions with supremum strictly smaller than 1. By Nina Zorboska. On the classification of homogeneous multipliers bounded on //'(R2). By James E. Daly Keith Phillips. On the second derivatives of convex functions on Hubert spaces. By Nobuyuki Kato... Isometries of spaces of weak* continuous functions. By Michael Cambern Krzysztof Jarosz. Canonical domains on Riemann surfaces. By Bernard Maskit. On metric spaces with uniform normal structure. By M. A. Khamsi. Weighted inequalities for Riemann-Liouville fractional integrals of order one greater. solutions for a class of radially symmetric By F. J. Martin-Reyes E. Sawyer. Non-negative non-positone problems. By Alfonso Castro R. Shivaji. A result on nearness of functions their regular C-fraction expansions. By Lisa Jacobsen Haakon Waadel. Weakly constricted operators Jamison's convergence theorem. By Robert Sine.. Existence nonexistence of radial limits of minimal surfaces. By Kirk E. Lancaster By Delin Tan. On two-generator discrete groups of Möbius transformations. By A. Bressan, Upper semicontinuous differential inclusions without convexity. A. Cellina G Colombo. A strong Parrott theorem. By Ciprian Foias Allen Tannenbaum. On oscillations of unbounded solutions. By I. Györi, G. Ladas L. Pakula D. GEOMETRY Remarks on the rigidity stability of minimal submanifolds. (Continued on inside back cover) By Makoto Sakaki. 793