Inverse problems for Einstein manifolds

Colin Guillarmou (1) , Antonio Sa Barreto (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 Purdue University [West Lafayette]

We show that the knowledge of the Dirichlet-to Neumann operator of the Laplacian on an open subset of the boundary of a compact Einstein manifold with boundary determines the manifold up to isometries. Similarly, for conformally compact Einstein manifolds, we prove that the knowledge of either the scattering operator at a certain fixed energy, or the Dirichlet-to-Neumann map for the conformal compactification, on an open subset of the boundary of the manifold, determines the manifold up to isometries.

Domaines: Géométrie différentielle [math.DG]

Colin Guillarmou, Antonio Sa Barreto. Inverse problems for Einstein manifolds. 2007. ⟨hal-00176966v1⟩