Mathematics

The classical boundary rigidity problem asks whether, or to what extent, the inner geometry of a compact Riemannian manifold with boundary can be determined by means of boundary measurements, such as the distance function among boundary points, or the geodesic scattering map. In my talk I will review this problem and some of the known results that are valid for "simple" Riemannian manifolds. I will then sketch the proof of some recent boundary rigidity results for non-simple Riemannian surfaces, including surfaces with trapped geodesics or with non-convex boundary. The talk is based on joint work with Colin Guillarmou and Leo Tzou.