Seminar on Differential Geometry. (AM-102), Volume 102 / / ed. by Shing-Tung Yau.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• MitwirkendeR: Aubin, Thierry,; Bakelman, I.,; Beem, John K.,; Bourguignon, Jean Pierre,; Calabi, Eugenio,; Chaohao, Gu,; Cheeger, Jeff,; Chen, Hsing-Hen,; DeTurck, Dennis M.,; Dodziuk, Jozef,; Ehrlich, Paul E.,; Gidas, Basilis,; Goresky, Mark,; Greene, R. E.,; Gromoll, Detlef,; Grove, Karsten,; Hildebrandt, Stefan,; Jacobowitz, H.,; Jaffe, Arthur,; Karp, Leon,; Kazdan, Jerry L.,; Lapedes, A. S.,; Lawson, H. Blaine,; Lee, Yee-Chun,; Li, Peter,; MacPherson, Robert,; Michelsohn, M. L.,; Ni, Wei-Ming,; Penrose, R.,; Perry, Malcolm J.,; Schoen, Richard,; Siu, Yum-Tong,; Teissier, B.,; Treibergs, Andrejs E.,; Uhlenbeck, Karen K.,; Wells, R. O.,; Yang, C. T.,; Yau, Shing-Tung,
• HerausgeberIn: Yau, Shing-Tung,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2016]; ©1982
• Year of Publication: 2016
• Language: English
• Series: Annals of Mathematics Studies ; 102
• Physical Description: 1 online resource (720 p.)

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 A...

Table of Contents

• Frontmatter
• TABLE OF CONTENTS
• INTRODUCTION
• SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY
• POINCARÉ INEQUALITIES ON RIEMANNIAN MANIFOLDS
• BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM
• LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS
• SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS
• AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS
• ON THE BLASCHKE CONJECTURE
• BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM
• GAUSSIAN AND SCALAR CURVATURE, AN UPDATE
• CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE
• RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER
• COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE
• ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE
• APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS
• EXTREMAL KÄHLER METRICS
• L2 HARMONIC FORMS ON COMPLETE MANIFOLDS
• L2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES
• FUNCTION THEORY OF NONCOMPACT KÄHLER MANIFOLDS OF NONPOSITIVE CURVATURE
• KÄHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS
• COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME
• LOCAL ISOMETRIC EMBEDDINGS
• YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS
• SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS
• ON PARALLEL YANG-MILLS FIELDS
• VARIATIONAL PROBLEMS FOR GAUGE FIELDS
• SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS
• THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM
• CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES
• RENORMALIZATION
• METRICS WITH PRESCRIBED RICCI CURVATURE
• BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY
• GRAVITATIONAL INSTANTONS
• SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY
• PROBLEM SECTION
• Backmatter