Mathematical Research Letters

Volume 11 (2004)

Number 3

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

Pages: 285 – 297

DOI: https://dx.doi.org/10.4310/MRL.2004.v11.n3.a2

Authors

Leonid Pestov (Russian Academy of Sciences)

Gunther Uhlmann (University of Washington, Seattle)

Abstract

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.

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Published 1 January 2004