Title:On the anisotropic Calderon problem on singular Riemannian manifolds of Painleve type: the borderline between uniqueness and invisibility.
Abstract: The anisotropic Calderon problem consists in determing the metric of a Riemannian manifold with boundary from the knowledge of its Dirichlet-to-Neumann map. I this talk, I will study this type of problem on Riemannian manifolds equiped with singular metrics, i.e. metrics whose coefficients are in some L^p spaces. In the particular case of Riemannian manifolds having certain separability properties of the geodesic flow (Painlevé property), I shall show what is the borderline between uniqueness and non-uniqueness results in the corresponding anisotropic Calderon problem. This is a joint work with Niky Kamran (McGIll) and Francois Nicoleau (Nantes).