Isospectral Riemannian manifolds with different local geometry
Dartmouth College
Wednesday, September 12
2:30-3:30 pm, Room 4422
To what extent does the spectrum of the Laplacian of a compact Riemannian
manifold determine its geometry? We will address this question by discussing
a method for constructing isospectral manifolds with different local geometry.
Examples will reveal various curvature properties which are not spectrally
determined.
For non-compact manifolds, one considers the scattering poles instead of the
spectrum (which need no longer be discrete). We construct continuous families
of isoscattering metrics given by compact perturbations of the Euclidean metric
on R^n.
Carolyn.S.Gordon@Dartmouth.edu