Geometry and Analysis on Manifolds: Proceedings of the 21st International Taniguchi Symposium held at Katata, Japan, Aug. 23–29 and the Conference held at Kyoto, Aug. 31–Sept. 2, 1987

Michael T. Anderson (auth.), Toshikazu Sunada (eds.)9780387501130, 0-387-50113-4

The Taniguchi Symposium on global analysis on manifolds focused mainly on the relationships between some geometric structures of manifolds and analysis, especially spectral analysis on noncompact manifolds. Included in the present volume are expanded versions of most of the invited lectures. In these original research articles, the reader will find up-to date accounts of the subject.

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Table of contents :
L 2 harmonic forms on complete Riemannian manifolds….Pages 1-19
Ricci-flat Kähler metrics on affine algebraic manifolds….Pages 20-31
On the multiplicy of the eigenvalues of the Laplacian….Pages 32-53
Riemann surfaces of large genus and large λ 1 ….Pages 54-63
Cayley graphs and planar isospectral domains….Pages 64-77
On the almost negatively curved 3-sphere….Pages 78-85
Vanishing theorems for tensor powers of a positive vector bundle….Pages 86-105
Decay of eigenfunctions on Riemannian manifolds….Pages 106-117
Stability and negativity for tangent sheaves of minimal Kähler spaces….Pages 118-126
An obstruction class and a representation of holomorphic automorphisms….Pages 127-141
Tensorial ergodicity of geodesic flows….Pages 142-157
Harmonic functions with growth conditions on a manifold of asymptotically nonnegative curvature I….Pages 158-181
Density theorems for closed orbits….Pages 182-202
L 2 -Index and resonances….Pages 203-211
Approximation of Green’s function in a region with many obstacles….Pages 212-225
Lower bounds of the essential spectrum of the Laplace-Beltrami operator and its application to complex geometry….Pages 226-247
Fundamental groups and Laplacians….Pages 248-277