Abstract
We show that the Dirichlet-to-Neumann operatorof the Laplacian on an open subset of the boundary of a connectedcompact Einstein manifold with boundary determines the manifold up to isometries. Similarly, for connected conformally compactEinstein 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.
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