Inverse problems for Einstein manifolds

Abstract

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.

Corrected version

References in corpus (1)

• Continuation unique a partir de l'infini conforme pour les metriques d'Einstein

Cited by in corpus (1)

• Invisibility and Inverse Problems