On the paper "Determining Anisotropic Real-Analytic Conductivities by Boundary Measurements," by Lee and Uhlmann

This paper shows that anisotropic real-analytic conductivities on certain manifolds can be determined up to isometry by boundary measurements, which is contained in the Dirichlet-to-Neumann maps. By giving a decomposition of Riemannian Laplacian into product of pseudo-differential operators, the proof first shows the Taylor series for the metric can be recovered from the DN map. Then given two anisotropic real-analytic conductivities with identical DN map, they are able to construct a diffeomorphism on the manifold by analytic continuation, under which the pullback of one conductivity is identical to the other.