Two dimensional compact simple Riemannian manifolds are boundary distance rigid

Abstract

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.

Authors

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