Two dimensional compact simple Riemannian manifolds are boundary distance rigid
Analysis of PDEs
2007-05-23 v1 Differential Geometry
Abstract
We prove that knowing the length of geodesics joining points on the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.
Cite
@article{arxiv.math/0305280,
title = {Two dimensional compact simple Riemannian manifolds are boundary distance rigid},
author = {L. Pestov and G. Uhlmann},
journal= {arXiv preprint arXiv:math/0305280},
year = {2007}
}