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 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.

Domaines: Géométrie différentielle [math.DG]

Colin Guillarmou, Antonio Sa Barreto. Inverse problems for Einstein manifolds. Inverse Problems and Imaging , 2009, pp.Vol 3, no 1, 1-15. ⟨hal-00176966v2⟩