VOLUME 119 NUMBER 1 SEPTEMBER 1993

PROCEEDINGS-A. OF THE

AMERICAN MATHEMATICAL SOCIETY

William Adams Barbara Lee Keyfitz,Dale Alspach Coordinating Editor for ODE,J. Marshall Ash PDE, Global Analysis, andAlbert Baernstein II Dynamical Systems

Eric Bedford Irwin Kra, Managing Editor

Andreas R. Blass Peter Li, Coordinating Editor

Andrew M. Bruckner for Lie Groups, Topology,

Christopher Croke and Geometry

Richard T. Durrett Wei Y. Loh

Clifford J. Earle Jr., Joseph S. B. MitchellCoordinating Editor for M. Susan Montgomery,

Analysis and Operator Theory Coordinating Editor for

Eric Friedlander Algebra, Number Theory,

Theodore W. Gamelin and Combinatorics

James Glimm, Coordinating Charles Pugh

Editor for Applied David SharpMathematics, Probability, Lance W. Small

and Statistics Hal L. SmithKen Goodearl Ronald M. Solomon

Roe Goodman Ronald Stern

Thomas Goodwillie Franklin D. Tall

Dennis A. Hejhal John Trangenstein

Palle E. T. Jorgensen Wolmer V. Vasconcelos

Jeffry N. Kahn James West

PROVIDENCE, RHODE ISLAND USA

ISSN 0002-9939

Proceedings of the American Mathematical Society

This journal is devoted entirely to research in pure and applied mathematics.

Subscription information. Proceedings of the American Mathematical Society is pub-lished monthly. Subscription prices for Volumes 117-119 (1993) are $538 list; $430institutional member; $323 individual member. A late charge of 10% of the subscrip-

tion price will be imposed upon orders received from nonmembers after January 1 of the

subscription year. Subscribers outside the United States and India must pay a postagesurcharge of $25; subscribers in India must pay a postage surcharge of $38. Expedited

delivery to destinations in North America—$38; elsewhere—$90.

Back number information. For back issues see the AMS Catalog of Publications.

Subscriptions and orders should be addressed to the American Mathematical Soci-

ety, P.O. Box 1571, Annex Station, Providence, RI 02901-1571. All orders must beaccompanied by payment. Other correspondence should be addressed to P. O. Box 6248,

Providence, RI 02940-6248.

Copying and reprinting. Individual readers of this publication, and nonprofit libraries

acting for them, are permitted to make fair use of the material, such as to copy an articlefor 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 Manager

of Editorial Services, American Mathematical Society, P. O. Box 6248, Providence, RI

02940-6248.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 ofthe U.S. Copyright Law, provided that a fee of $1.00 plus $.25 per page for each copy

be paid directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem, MA

01970. This consent does not extend to other kinds of copying, such as copying for

general distribution, for advertising or promotion purposes, for creating new collectiveworks, or for resale.

Proceedings of the American Mathematical Society is published monthly by the Amer-

ican Mathematical Society at 201 Charles Street, Providence, RI 02904-2213. Second-class postage is paid at Providence, Rhode Island. Postmaster: Send address changes toProceedings, American Mathematical Society, P. O. Box 6248, Providence,' RI 02940-

6248.

Copyright ©1993 by the American Mathematical Society. All rights reserved.Printed in the United States of America.

The paper used in this journal is acid-free and falls within the guidelinesestablished to ensure permanence and durability. ©

This publication was typeset using A\4S-Tt~X,

the American Mathematical Society's TgX macro system.

10 9 8 7 6 5 4 3 2 1 98 97 96 95 94 93

Editorial Information

To be published in the Proceedings, a paper must be correct, new, nontrivial,

and significant. Further, it must be well written and of interest to a substantialnumber 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 solicit and

encourage publication of worthy papers of length not exceeding 10 published

pages. Published pages are the same size as those generated in the style files

provided for A\jS-Tt^X or AmS-I^T^X.

Very short notes not to exceed two printed pages are also accepted, and appear

under the heading Shorter Notes. Items deemed suitable include an elegant

new proof of an important and well-known theorem, an illuminating example

or counterexample, or a new viewpoint on familiar results. New results, if of

a brief and 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.

As of June 3, 1993, the backlog for this journal was approximately 12 issues.

This estimate is the result of dividing the number of manuscripts for this journalin the Providence office that have not yet gone to the printer on the above date

by the average number of articles per issue over the previous twelve months,

reduced by the number of issues published in four months (the time necessary

for editing and composing a typical issue).

A Copyright Transfer Agreement is required before a paper will be publishedin this journal. By submitting a paper to this journal, authors certify that the

manuscript has not been submitted to nor is it under consideration for publi-cation by another journal, conference proceedings, or similar publication.

Information for Authors and Editors

The first page of an article must consist of a descriptive title, followed by

an abstract that 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

"concern-

ing" should be avoided. The abstract should be at least one complete sentence,

and at most 150 words. Included with the footnotes to the paper, there should

be the 1991 Mathematics Subject Classification representing the primary and

secondary subjects of the article. This may be followed by a list of key words

and phrases describing the subject matter of the article and taken from it. A

list of the numbers may be found in the annual index of Mathematical Reviews,

published with the December issue starting in 1990, as well as from the elec-

tronic service e-MATH [telnet e-MATH.ams.org (or telnet 130.44.1.100). Login

and password are e-math]. For journal abbreviations used in bibliographies,

see the list of serials in the latest Mathematical Reviews annual index. When

the manuscript is submitted, authors should supply the editor with electronic

addresses if available. These will be printed after the postal address at the end

of each article.

Two copies of the paper should be sent directly to the appropriate Editor and

the author should keep one copy.

Electronically prepared manuscripts. The AMS encourages submission of elec-

tronically prepared manuscripts in AmS-T^X. or A^jS-M^X because properly

prepared electronic manuscripts save the author proofreading time and move

more quickly through the production process. To this end, the Society has pre-

pared "preprint"

style files, specifically the amsppt style of «4a^<S-T£X and the

amsart style of AMS-URgX., which will simplify the work of authors and of the

production staff. Those authors who make use of these style files from the be-

ginning of the writing process will further reduce their own effort. Electronically

submitted manuscripts prepared in plain T£X or IaTeX do not mesh properlywith the AMS production systems and cannot, therefore, realize the same kind

of expedited processing. Users of plain TgX should have little difficulty learning

^Vt^-TgX, and J4TrfX users will find that AmS-1£TeX is the same as lATpX with

additional commands to simplify the typesetting of mathematics.

Guidelines for Preparing Electronic Manuscripts provides additional assis-

tance and is available for use with either AmS-T^X or AmS-MTeX- Authors withFTP access may obtain Guidelines from the Society's Internet node

e-MATH@math.ams.org (130.44.1.100). For those without FTP access Guide-lines can be obtained free of charge from the e-mail address guide-elec@math.ams.org (Internet) or from the Publications Department, American Math-

ematical Society, P.O. Box 6248, Providence, RI 02940-6248. When requestingGuidelines, please specify which version you want.

At the time of submission, authors should indicate if the paper has been pre-

pared using AmS-TtjX or „4a/1<S-IaTe;X. The Manual for Authors of Mathematical

Papers should be consulted for symbols and style conventions. The Manual may

be obtained free of charge from the e-mail address cust-serv@math.ams.org or

from the Customer Services Department, American Mathematical Society, P.O.

Box 6248, Providence, RI 02940-6248. The Providence office should be sup-

plied with a manuscript that corresponds to the electronic file being submitted.Electronic manuscripts should be sent to the Providence office immediately

after the paper has been accepted for publication. They can be sent via e-mail

to pub-submit@math.ams.org (Internet) or on diskettes to the Publications De-

partment address listed above. When submitting electronic manuscripts pleasebe sure to include a message indicating in which publication the paper has been

accepted. No corrections will be accepted electronically. Authors must mark

their changes on their proof copies and return them to the Providence office.

Authors and editors are encouraged to make the necessary submissions of elec-

tronically prepared manuscripts and proof copies in a timely fashion.

Any inquiries concerning a paper that has been accepted for publicationshould be sent directly to the Editorial Department, American Mathematical

Society, P. O. Box 6248, Providence, RI 02940-6248.

Editors

Authors are requested to send papers directly to the appropriate Editor (the one whose area ofresponsibility and expertise, as described below, most closely approximates the subject field of the

manuscript). Only when in doubt about an appropriate Editor, should manuscripts be sent to the

Coordinating Editor responsible for the area in mathematics most closely connected to the paper. If

in doubt about the area, send manuscript to the Managing Editor, to whom all other communication

about the journal should also be addressed. (All addresses should include the line "Department

of

Mathematics", unless another department is indicated.)

Managing Editor: Irwin Kra, SUNY at Stony Brook, Stony Brook, NY 11794-3651e-mail: irwin@math.sunysb.edu

1. ODE, PDE, GLOBAL ANALYSIS, AND DYNAMICAL SYSTEMSCoordinating Editor: Barbara Lee Keyfitz, University of Houston, Houston, TX 77204-3476,

e-mail: keyfitz@uh.edu

Partial differential equations, Barbara Lee Keyfitz

Dynamical systems and global analysis, Charles Pugh, University of California at Berkeley,

Berkeley, CA 94720

Ordinary differential equations and special functions, Hal L. Smith, Arizona State University,Tempe, AZ 85287, e-mail: athls@asuacad.bitnet

2. LIE GROUPS, TOPOLOGY, AND GEOMETRYCoordinating Editor: Peter Li, University of California, Irvine, CA 92717,e-mail: pli@orion.oac.uci.edu

Topological groups and Lie groups (symmetric spaces), Roe Goodman, Rutgers University,New Brunswick, NJ 08903, e-mail: goodman@math.rutgers.edu

Riemannian geometry (including aftine, pseudo-Riemannian, contact, classical, and Lorentzian ge-ometries), Christopher Croke, University of Pennsylvania, Philadelphia, PA 19104,

e-mail: ccroke@math.upenn.edu

Geometric analysis (geometric PDE, minimal surfaces, harmonic maps) and Kahler geometry, Peter

Li

Algebraic topology (higher dimensional topology), Thomas Goodwillie, Brown University, Box1917, Providence, RI 02912, e-mail: tomg@brownvm.bitnet

Metric and geometric topology, James West, Cornell University, White Hall, Ithaca, NY 14853-

7901, e-mail: west@mssun7.msi.cornell.edu

Set-theoretic and general topology, Franklin D. Tall, University of Toronto, Toronto, Ontario,

Canada M5S 1A1, e-mail: tall@math.toronto.edu

Low dimensional topology and differential topology (knot theory, 3- and 4-manifolds, Gauge-

theory), Ronald Stern, University of California, Irvine, CA 92717, e-mail: rstern@math.uci.edu

3. ANALYSIS AND OPERATOR THEORYCoordinating Editor: Clifford J. Earle, Jr., Cornell University, White Hall, Ithaca, NY 14853,e-mail: cliff@math.cornell.edu

One complex variable and potential theory, Albert Baernstein II, Washington University, St. Louis,

MO 63130, e-mail: C31801AB@WUVMD.BITNET

Several complex variables, Eric Bedford, Indiana University, Swain Hall East, Bloomington, IN

47401, e-mail: BEDFORD@ucs.indiana.edu

Functional analysis and operator theory, Palle E. T. Jorgensen, University of Iowa, Iowa City, IA

52242

Functional analysis, Dale Alspach, Oklahoma State University, Stillwater, OK 74078,

e-mail: alspach@hilbert.math.okstate.edu

Complex variables, functional analysis, and operator theory, Theodore W. Gamelin, UCLA,

Los Angeles, CA 90024, e-mail: twg@math.ucla.edu

Real analysis, Andrew Bruckner, University of California, Santa Barbara, CA 93106,

e-mail: bruckner@math.ucsb.edu

Harmonic and general analysis, J. Marshall Ash, DePaul University, Chicago, IL 60614,

e-mail: MATJMA@DEPAUL.BITNET

Analytic number theory and automorphic forms, Dennis A. Hejhal, School of Mathematics,

University of Minnesota, Minneapolis, MN 55455, e-mail: mfl0402@uc.msc.umn.edu

4. ALGEBRA, NUMBER THEORY, AND COMBINATORICSCoordinating Editor: M. Susan Montgomery, University of Southern California, DRB 155,Los Angeles, CA 90089-1113, e-mail: smontgom@math.usc.edu

General number theory, William Adams, University of Maryland, College Park, MD 20742,e-mail: wwa@nina.umd.edu

General algebra, Lance W. Small, University of California San Diego, La Jolla, CA 92093-0112,e-mail: lwsmall@ucsd.edu

Commutative algebra, Wolmer V. Vasconcelos, Rutgers University, New Brunswick, NJ 08903,e-mail: vasconcelos@math.rutgers.edu

Group theory, Ronald M. Solomon, Ohio State University, Columbus, OH 43210,e-mail: solomon@function.mps.ohio-state.edu

/^-theory, algebraic groups, algebraic geometry, Eric Friedlander, Northwestern University, Evanston.IL 60208, e-mail: eric@math.nwu.edu

Combinatorics, Jeffry N. Kahn, Rutgers University, New Brunswick, NJ 08903,e-mail: jkahn@elbereth.rutgers.edu

Analytic number theory and automorphic forms, Dennis A. Hejhal, School of Mathematics,University of Minnesota, Minneapolis, MN 55455, e-mail: mfl0402@uc.msc.umn.edu

Logic and foundations, Andreas R. Blass, University of Michigan, Ann Arbor, MI 48109-1003,e-mail: Andreas. R._ Blass@ub.cc.umich.edu

Lie algebras and Lie groups, Roe Goodman. Rutgers University, New Brunswick, NJ 08903,e-mail: goodman@math.rutgers.edu

Noncommutative rings, Ken Goodearl, University of California, Santa Barbara, CA 93106,e-mail: goodearl@math.ucsb.edu

5. APPLIED MATHEMATICS, PROBABILITY, AND STATISTICSCoordinating Editor: James Glimm, Department of Applied Mathematics and Statistics, SUNYat Stony Brook, Stony Brook, NY 11794-3600, e-mail: glimm@ams.sunysb.edu

Probability, Richard T. Durrett, Cornell University, White Hall, Ithaca, NY 14853-7901, e-mail:rtd@cornella.cit.cornell.edu

Statistics, Wei Y. Loh, Department of Statistics, University of Wisconsin, 1210 W. DaytonStreet, Madison, WI 53706, e-mail: loh@stat.wisc.edu

Applied mathematics, David Sharp, Theoretic Division, Los Alamos National Laboratory MSB285.Los Alamos, NM 87545, e-mail:dhs@lanl.gov

John Trangenstein, Duke University, Durham, NC 27706, e-mail: johnt@math.duke.edu

Operations research, Joseph S. B. Mitchell, Department of Applied Mathematics and Statistics,SUNY at Stony Brook, Stony Brook, NY 11794-3600, e-mail: jsbm@ams.sunysb.edu

{Continued from back cover)

On some cubic modular identities. By Li-Chien Shen. 203

Almost isometric copies of loo in some Banach spaces. By H. Hudzik and M. MastyLo 209

The stable neighborhood theorem and lengths of closed geodesies. By Ara Basmajian . . 217

Potential space estimates for Green potentials in convex domains. By Stephen J. Fromm 225

Discreteness of some continuous spectrum eigenfunction expansions. By Don B. Hinton

and Robert M. Kauffman. 235

D. GEOMETRY

Minimal surfaces and //-surfaces in nonpositively curved space forms. By Bennett

Palmer. 245

Some deformations of the Hopf foliation are also Kahler. By Paul D. Scofield . 251

Projectively flat surfaces in A3. By Fabio Podesta. 255

Complete minimal surfaces and the puncture number problem. By Kichoon Yang ... 261

E. LOGIC AND FOUNDATIONS

Adding dominating reals with the random algebra. By Haim Judah and Saharon Shelah 267

Certain games, category, and measure. By S-lawomir Solecki. 275

G. TOPOLOGY

On weakly chainable inverse limits with simplicial bonding maps. By Piotr Minc. 281

Closures of weakened analytic groups. By T. Christine Stevens. 291

Finite loop spaces with maximal tori have finite Weyl groups. By Larry Smith . 299

A cyclic monotonically normal space which is not K0. By Mary Ellen Rudin. 303

Lyapunov characteristic exponents are nonnegative. By Feliks Przytycki. 309

An equivariant construction. By Pedro L. Q. Pergher. 319

Every attractor of a flow on a manifold has the shape of a finite polyhedron. By Bernd

Gunther and Jack Segal. 321

On ^-extensions of developable spaces. By T. Mizokami. 331

SHORTER NOTES

The Hayman-Wu constant. By Knut 0yma . 337

Approximate continuity and linear approximate continuity. By Casper Goffman. 339

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

CONTENTS

Vol. 119, No. 1 Whole No. 411 September 1993

A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS

Injective morphisms of afnne varieties. By Ming-chang Kang . 1

On infinite disjoint covering systems. By Aviezri S. Fraenkel and R. Jamie Simpson . 5

Vanishing theorems for singular varieties. By Kyungho Oh. 11

A numerical characterization of hypersurface singularities. By Juan Elias . 15

Local isogeny theorem for Drinfeld modules with nonintegral invariants. By Sunghan

Bae and Pyung-Lyun Kang. 19

The length of elements in free solvable groups. By Carl Droms, Jacques Lewin, and

Herman Servatius. 27

Special values of the Lerch zeta function and the evaluation of certain integrals. By

Kenneth S. Williams and Zhang Nan-Yue. 35

The special values at negative integers of Dirichlet series associated with polynomials of

several variables. By Minking Eie. 51"Complete-simple"

distributive lattices. By G. Gratzer and E. T. Schmidt. 63

Some studies on n-coherent rings. By Mingyi Wang. 71

On groups related to the Hecke groups. By Marvin I. Knopp and Morris Newman ... 77

Linear transformations preserving potent matrices. By Matej Bresar and Peter Semrl 81

Symmetric nilpotent matrices with maximal rank and a conjecture of Grothendieck-Koblitz.

By Ching-Li Chai; Appendix by Michael Larsen. 87

B. ANALYSIS

Finite moments perturbations of y" = 0 in Banach algebras. By Renato Spigler and

Marco Vianello. 97

The Hausdorff dimension of the nondifferentiability set of the Cantor function is

[ln(2)/ln(3)]2. By Richard Darst. 105

Univalent harmonic mappings onA={z:|z|>l). By Sook Heui Jun . 109

On sets nonmeasurable with respect to invariant measures. By S-lawomir Solecki .... 115

Integrability of reciprocals of the Green's function for elliptic operators: counterexamples.

By M. Cristina Cerutti. 125

Automatic continuity of homomorphisms in topological algebras. By S. J. Bhatt. 135

Subspaces and graphs. By Kin Yan Chung. 141

Weakly continuous functions on Banach spaces not containing l\. By Joaquin M.

Gutierrez. 147

The Hankel transformation of Banach-space-valued generalized functions. By E. L. Koh

and C. K. Li. 153

Locally finite-dimensional sets of operators. By Leonya Livshits. 165

Invariant subspaces of Toeplitz operators with piecewise continuous symbols. By Vladimir

V. Peller. 171

Existence of a nontrivial solution to a strongly indefinite semilinear equation. By

B. Buffoni, L. Jeanjean, and C. A. Stuart. 179

On subadditive functions. By Janusz Matkowski and Tadeusz Swiatkowski. 187

Some estimates for harmonic measures. III. By James A. Jenkins. 199

{Continued on inside back cover)

0002-9939(199309)119:1;1-U