  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.
