Mathematical Research Letters
Volume 11 (2004)
The boundary distance function and the Dirichlet-to-Neumann map
Pages: 285 – 297
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.