Seminar on Differential Geometry. (AM-102), Volume 102 / Shing-tung Yau.

Format:

Book

Contributor:

Institute for Advanced Study (Princeton, N.J.)

Yau, Shing-tung, editor.

Series:

Annals of mathematics studies ; Number 102.

Annals of Mathematics Studies ; 279

Language:

English

Subjects (All):

Geometry, Differential.

Differential equations, Partial.

Physical Description:

1 online resource (721 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.

Contents:

Frontmatter

TABLE OF CONTENTS

INTRODUCTION

SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY / Yau, Shing-Tung

POINCARÉ INEQUALITIES ON RIEMANNIAN MANIFOLDS / Li, Peter

BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM / Teissier, B.

LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS / Hildebrandt, Stefan

SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS / Karp, Leon

AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS / Kazdan, Jerry L.

ON THE BLASCHKE CONJECTURE / Yang, C. T.

BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM / Aubin, Thierry

GAUSSIAN AND SCALAR CURVATURE, AN UPDATE / Kazdan, Jerry L.

CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE / Ni, Wei-Ming

RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER / Gromoll, Detlef / Grove, Karsten

COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE / Schoen, Richard / Yau, Shing-Tung

ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE / Treibergs, Andrejs E.

APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS / Bakelman, I.

EXTREMAL KÄHLER METRICS / Calabi, Eugenio

L2 HARMONIC FORMS ON COMPLETE MANIFOLDS / Dodziuk, Jozef

L2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES / Cheeger, Jeff / Goresky, Mark / MacPherson, Robert

FUNCTION THEORY OF NONCOMPACT KÄHLER MANIFOLDS OF NONPOSITIVE CURVATURE / Greene, R. E.

KÄHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS / Michelsohn, M. L.

COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME / Siu, Yum-Tong / Yau, Shing-Tung

LOCAL ISOMETRIC EMBEDDINGS / Jacobowitz, H.

YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS / Bourguignon, Jean Pierre / Lawson, H. Blaine

SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS / Gidas, Basilis

ON PARALLEL YANG-MILLS FIELDS / Chaohao, Gu

VARIATIONAL PROBLEMS FOR GAUGE FIELDS / Uhlenbeck, Karen K.

SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS / Chen, Hsing-Hen / Lee, Yee-Chun

THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM / Wells, R. O.

CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES / Beem, John K. / Ehrlich, Paul E.

RENORMALIZATION / Jaffe, Arthur

METRICS WITH PRESCRIBED RICCI CURVATURE / DeTurck, Dennis M.

BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY / Lapedes, A. S.

GRAVITATIONAL INSTANTONS / Perry, Malcolm J.

SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY / Penrose, R.

PROBLEM SECTION / Yau, Shing-Tung

Backmatter

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

1-4008-8191-9

OCLC:

979579219