Mathematical Research Letters

Volume 11, Issue 3, May 2004 pp. 285-297.

The boundary distance function and the Dirichlet-to-Neumann map

Authors: Leonid Pestov and Gunther Uhlmann
Author institution: Russian Academy of Sciences, and University of Washington, Seattle

Summary: We outline the proof that two dimensional simple Riemannian manifolds with boundary are boundary distance rigid. In addition we give, in two dimensions, a reconstruction procedure to recover the index of refraction of a bounded medium in Euclidean space from the travel times of sound waves going through the medium.

Contents Full-Text PDF