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Inverse problems for Einstein manifolds

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  • We show that the Dirichlet-to-Neumann operator of the Laplacian on an open subset of the boundary of a connected compact Einstein manifold with boundary determines the manifold up to isometries. Similarly, for connected conformally compact Einstein manifolds of even dimension $n+1,$ we prove that the scattering matrix at energy $n$ on an open subset of its boundary determines the manifold up to isometries.
    Mathematics Subject Classification: Primary 58J50, Secondary 35P25.

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