Two dimensional compact simple Riemannian manifolds are boundary distance rigid


We prove that knowing the lengths of geodesics joining points of the boundary of a two-dimensional, compact, simple Riemannian manifold with boundary, we can determine uniquely the Riemannian metric up to the natural obstruction.


Leonid Pestov

UGRA Research Institute of Information Technologies, Hanty-Mansiysk 628011, Russian Federation

Gunther Uhlmann

Department of Mathematics, University of Washington, Seattle, WA 98195, United States