Seminar on differential geometry

Cover......Page 1
Title Page......Page 4
Copyright Page......Page 5
TABLE OF CONTENTS......Page 6
INTRODUCTION......Page 10
SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN DIFFERENTIAL GEOMETRY......Page 14
POINCARE INEQUALITIES ON RIEMANNIAN MANIFOLDS......Page 84
BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I. INTRODUCTION TO THE PROBLEM......Page 96
LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS......Page 118
SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS......Page 144
AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS......Page 154
ON THE BLASCHKE CONJECTURE......Page 170
BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM: THE YAMABE PROBLEM......Page 184
GAUSSIAN AND SCALAR CURVATURE, AN UPDATE......Page 196
CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE......Page 204
RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER......Page 214
COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE......Page 220
ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE......Page 240
APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS......Page 250
EXTREMAL KAHLER METRICS......Page 270
L^2 HARMONIC FORMS ON COMPLETE MANIFOLDS......Page 302
L^2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES......Page 314
FUNCTION THEORY OF NONCOMPACT KAHLER MANIFOLDS OF NONPOSITIVE CURVATURE......Page 352
KAHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS......Page 370
COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME......Page 374
LOCAL ISOMETRIC EMBEDDINGS......Page 392
YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS......Page 406
SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS......Page 434
ON PARALLEL YANG-MILLS FIELDS......Page 454
VARIATIONAL PROBLEMS FOR GAUGE FIELDS......Page 466
SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS......Page 476
THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM......Page 494
CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLETENESS FOR STRONGLY CAUSAL SPACE-TIMES......Page 510
RENORMALIZATION......Page 518
METRICS WITH PRESCRIBED RICCI CURVATURE......Page 536
BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY......Page 550
GRAVITATIONAL INSTANTONS......Page 614
SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY......Page 642
PROBLEM SECTION......Page 680