Geometry and Topology Seminar

For analytic negatively curved compact connected Riemannian manifold with analytic strictly convex boundary, the scattering map for the geodesic flow determines the manifold up to isometry. After detailing this result, I will explain how it can be proved using a unique continuation principle. This requires to know that certain objects are real-analytic: I will give a hint on the method of real-analytic microlocal analysis that we used to prove it. This is a joint work with Yannick Guedes Bonthonneau  and Colin Guillarmou.