Forward and Inverse Scattering on Manifolds with Asymptotically Cylindrical Ends
نویسندگان
چکیده
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) + 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) +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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