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THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM

© 2016 Princeton University Press, Princeton

© 2016 Princeton University Press, Princeton

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. INTRODUCTION ix
  4. SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY 1
  5. POINCARÉ INEQUALITIES ON RIEMANNIAN MANIFOLDS 73
  6. BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM 85
  7. LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS 107
  8. SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS 133
  9. AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS 143
  10. ON THE BLASCHKE CONJECTURE 159
  11. BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM 173
  12. GAUSSIAN AND SCALAR CURVATURE, AN UPDATE 185
  13. CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE 193
  14. RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER 203
  15. COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE 209
  16. ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE 229
  17. APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS 239
  18. EXTREMAL KÄHLER METRICS 259
  19. L2 HARMONIC FORMS ON COMPLETE MANIFOLDS 291
  20. L2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES 303
  21. FUNCTION THEORY OF NONCOMPACT KÄHLER MANIFOLDS OF NONPOSITIVE CURVATURE 341
  22. KÄHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS 359
  23. COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME 363
  24. LOCAL ISOMETRIC EMBEDDINGS 381
  25. YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS 395
  26. SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS 423
  27. ON PARALLEL YANG-MILLS FIELDS 443
  28. VARIATIONAL PROBLEMS FOR GAUGE FIELDS 455
  29. SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS 465
  30. THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM 483
  31. CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES 499
  32. RENORMALIZATION 507
  33. METRICS WITH PRESCRIBED RICCI CURVATURE 525
  34. BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY 539
  35. GRAVITATIONAL INSTANTONS 603
  36. SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY 631
  37. PROBLEM SECTION 669
  38. Backmatter 707
Seminar on Differential Geometry
This chapter is in the book Seminar on Differential Geometry
https://doi.org/10.1515/9781400881918-028

Chapters in this book

  1. Frontmatter i
  2. TABLE OF CONTENTS v
  3. INTRODUCTION ix
  4. SURVEY ON PARTIAL DIFFERENTIAL EQUATIONS IN 3 DIFFERENTIAL GEOMETRY 1
  5. POINCARÉ INEQUALITIES ON RIEMANNIAN MANIFOLDS 73
  6. BONNESEN-TYPE INEQUALITIES IN ALGEBRAIC GEOMETRY, I: INTRODUCTION TO THE PROBLEM 85
  7. LIOUVILLE THEOREMS FOR HARMONIC MAPPINGS, AND AN APPROACH TO BERNSTEIN THEOREMS 107
  8. SUBHARMONIC FUNCTIONS, HARMONIC MAPPINGS AND ISOMETRIC IMMERSIONS 133
  9. AN ISOPERIMETRIC INEQUALITY AND WIEDERSEHEN MANIFOLDS 143
  10. ON THE BLASCHKE CONJECTURE 159
  11. BEST CONSTANTS IN THE SOBOLEV IMBEDDING THEOREM THE Y AMABE PROBLEM 173
  12. GAUSSIAN AND SCALAR CURVATURE, AN UPDATE 185
  13. CONFORMAL METRICS WITH ZERO SCALAR CURVATURE AND A SYMMETRIZATION PROCESS VIA MAXIMUM PRINCIPLE 193
  14. RIGIDITY OF POSITIVELY CURVED MANIFOLDS WITH LARGE DIAMETER 203
  15. COMPLETE THREE DIMENSIONAL MANIFOLDS WITH POSITIVE RICCI CURVATURE AND SCALAR CURVATURE 209
  16. ENTIRE SPACELIKE HYPERSURFACES OF CONSTANT MEAN CURVATURE IN MINKOWSKI SPACE 229
  17. APPLICATIONS OF THE MONGE-AMPERE OPERATORS TO THE DIRICHLET PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS 239
  18. EXTREMAL KÄHLER METRICS 259
  19. L2 HARMONIC FORMS ON COMPLETE MANIFOLDS 291
  20. L2-COHOMOLOGY AND INTERSECTION HOMOLOGY OF SINGULAR ALGEBRAIC VARIETIES 303
  21. FUNCTION THEORY OF NONCOMPACT KÄHLER MANIFOLDS OF NONPOSITIVE CURVATURE 341
  22. KÄHLER MANIFOLDS WITH VANISHING FIRST CHERN CLASS 359
  23. COMPACTIFICATION OF NEGATIVELY CURVED COMPLETE KAHLER MANIFOLDS OF FINITE VOLUME 363
  24. LOCAL ISOMETRIC EMBEDDINGS 381
  25. YANG-MILLS THEORY: ITS PHYSICAL ORIGINS AND DIFFERENTIAL GEOMETRIC ASPECTS 395
  26. SYMMETRY AND ISOLATED SINGULARITIES OF CONFORMALLY FLAT METRICS AND OF SOLUTIONS OF THE YANG-MILLS EQUATIONS 423
  27. ON PARALLEL YANG-MILLS FIELDS 443
  28. VARIATIONAL PROBLEMS FOR GAUGE FIELDS 455
  29. SOME GEOMETRICAL ASPECTS OF INTEGRABLE NONLINEAR EVOLUTION EQUATIONS 465
  30. THE CONFORMALLY INVARIANT LAPLACIAN AND THE INSTANTON VANISHING THEOREM 483
  31. CAUSALLY DISCONNECTING SETS, MAXIMAL GEODESICS AND GEODESIC INCOMPLET-ENESS FOR STRONGLY CAUSAL SPACE-TIMES 499
  32. RENORMALIZATION 507
  33. METRICS WITH PRESCRIBED RICCI CURVATURE 525
  34. BLACK HOLE UNIQUENESS THEOREMS IN CLASSICAL AND QUANTUM GRAVITY 539
  35. GRAVITATIONAL INSTANTONS 603
  36. SOME UNSOLVED PROBLEMS IN CLASSICAL GENERAL RELATIVITY 631
  37. PROBLEM SECTION 669
  38. Backmatter 707
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