Stability estimates in inverse problems for the Schrödinger and wave equations with trapping

Abstract

For a class of Riemannian manifolds with boundary that includes all negatively curved manifolds with strictly convex boundary, we establish Hölder type stability estimates in the geometric inverse problem of determining the electric potential or the conformal factor from the Dirichlet-to-Neumann map associated with the Schrödinger equation and the wave equation. The novelty in this result lies in the fact that we allow some geodesics to be trapped inside the manifold and have infinite length.