Forward and inverse scattering on manifolds with asymptotically cylindrical ends |
| |
Authors: | Hiroshi Isozaki Matti Lassas |
| |
Institution: | a Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan b Department of Mathematics, University College of London, United Kingdom c Department of Mathematics and Statistics, University of Helsinki, Finland |
| |
Abstract: | 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 2(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 2(dy)+h(x,dx). Given two such manifolds having the same scattering matrix on that exactly cylindrical end for all energies, we show that these two manifolds are isometric. |
| |
Keywords: | Scattering theory Inverse problems Riemannian manifolds Cylindrical ends |
本文献已被 ScienceDirect 等数据库收录! |
|