Forward and inverse scattering on manifolds with asymptotically cylindrical ends

Details Forward and inverse scattering on manifolds with asymptotically cylindrical ends Forward and inverse scattering on manifolds with asymptotically cylindrical ends

2009-05-11

arxiv.org/abs/0905.1571v1

Mathematics

Analysis of PDEs

Scientific paper

We study an inverse problem for a non-compact Riemannian manifold whose ends have the following properties : On each end, the Riemannian metric is assumed to be a short-range perturbation of the metric of the form $(dy)^2 + h(x,dx)$, $h(x,dx)$ being the metric of some compact manifold of codimension 1. Moreover one end is exactly cylindrical, i.e. the metric is equal to $(dy)^2 + h(x,dx)$. Given two such manifolds having the same scattering matrix on that exactly cylindrical end for all energy, we show that these two manifolds are isometric.

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