Inverse scattering on non-compact manifolds with general metric

Abstract: We consider a class of non-compact Riemannian manifolds, as large as possible, whose Laplacian has a continuous spectrum, and show that the associated scattering matrix determines the manifold, its topology and Riemannian metric. Knowledge of one end is sufficient to determine the whole manifold. If the end is a cusp, by introducing a generalized S-matrix, one can derive the same conclusion. We can also allow conic singularities for our manifolds so that they include Riemannian orbifolds. As for the volume growth of each end, it can be polynomially or exponentially increasing or decreasing. So, it is a natural largest class of manifolds on which we can develop the spectral and scattering theory. This is a joint work with Matti Lassas (and Yaroslav Kurylev).

Mathematics

Audience: researchers in the topic

International Zoom Inverse Problems Seminar, UC Irvine