Reconstruction of a compact Riemannian manifold from the scattering data of internal sources
Differential Geometry
2018-03-20 v2
Abstract
Given a smooth non-trapping compact manifold with strictly con- vex boundary, we consider an inverse problem of reconstructing the manifold from the scattering data initiated from internal sources. This data consist of the exit directions of geodesics that are emaneted from interior points of the manifold. We show that under certain generic assumption of the metric, one can reconstruct an isometric copy of the manifold from such scattering data measured on the boundary.
Cite
@article{arxiv.1708.07573,
title = {Reconstruction of a compact Riemannian manifold from the scattering data of internal sources},
author = {Matti Lassas and Teemu Saksala and Hanming Zhou},
journal= {arXiv preprint arXiv:1708.07573},
year = {2018}
}