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

Ruirui Wu, University of Washington
Thursday, March 9, 2023 - 12:30pm to 1:30pm
PDL C-401
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.