Scattering rigidity for analytic metrics

Abstract

For analytic negatively curved Riemannian manifold with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isometry. In particular one recovers both the topology and the metric. More generally, our result holds in the analytic category under the no conjugate point and hyperbolic trapped sets assumptions.

v2: added Propositions 2.6 and 2.7 and Appendix B v3: Electronic copy of final peer-reviewed manuscript accepted for publication