2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170582We 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.Corrected versionDifferential Geometry35R30text