Determinants and extremal metrics in conformal geometry

Kapitel in diesem Buch

1. I-IV I
2. Preface V
3. Table of Contents VII
4. Gauss-Manin connexions, logarithmic forms and hypergeometric functions 1
5. Laws of trigonometry in symmetric spaces 23
6. Determinants and extremal metrics in conformal geometry 37
7. The infinity behavior of the solutions to the harmonic map heat equation 59
8. On the absence of critical dimensions for the subelliptic Laplacian on the Heisenberg group 69
9. Minimal triangulation, complementarity and projective planes 77
10. Compact infrasolvmanifolds are smoothly rigid 85
11. Informal note on topology, geometry and topological field theory 99
12. Singularity theory for Riemannian distance functions on non-positively curved surfaces 117
13. The Gromov-Lawson-Rosenberg conjecture: when do manifolds admit metrics of positive scalar curvature 149
14. Geometry of the Radon-Penrose transform and interpretation of singularities 159
15. Realization in the large in R3 of surfaces 173
16. Borsuk-Ulam type theorems and systems of bilinear equations 183
17. Generalized affine rotation surfaces with geodesic orbits 195
18. Lower bounds on some geometric quantities and applications 207
19. Wavelet geometric analysis of the Dirichlet problem 219
20. Moser's inequality and n-Laplacian 237
21. Submanifold of a Riemannian manifold with semisymmetric recurrent connections 247
22. Frénet theorem for spaces of constant curvature 253
23. The generalized theorem of Castelnuovo-de Franchis for unitary representations 261
24. Poisson and symplectic geometry on loop spaces of smooth manifolds 285
25. An algebraic geometry view of a model quantum field theory on a curve 311
26. Deforming convex hypersurfaces by the linear combination of the mean curvature and the square root of the scalar curvature 331
27. Asymptotics for exterior solutions of quasilinear elliptic equations 343
28. External geometry of p-minimal surfaces 363
29. Geometry of torus quasi bundles over curves 377
30. Stability of minimal graphs in products of surfaces 395
31. Log Fano threefolds and quotients of K3 surfaces 403
32. On certain Laplace inequalities on manifolds 415
33. List of Participants 423
34. List of Contributors 429