RECOVERY OF TRANSVERSAL METRIC TENSOR IN THE SCHRO spacing diaeresis DINGER EQUATION FROM THE DIRICHLET-TO-NEUMANN MAP

In this paper, we deal with the inverse problem of determining simple metrics on a compact Riemannian manifold from boundary measurements. We take this information in the dynamical Dirichlet-to-Neumann map associated to the Schrodinger equation. We prove in dimension n > 2 that the knowledge of the Dirichlet-to-Neumann map for the Schrodinger equation uniquely determines the simple metric (up to an admissible set). We also prove a Holder-type stability estimate by the construction of geometrical optics solutions of the Schrodinger equation and the direct use of the invertibility of the geodesical X-ray transform.