Scattering rigidity for analytic metrics
Differential Geometry
2024-02-09 v3 Analysis of PDEs
Dynamical Systems
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.
Cite
@article{arxiv.2201.02100,
title = {Scattering rigidity for analytic metrics},
author = {Yannick Guedes Bonthonneau and Colin Guillarmou and Malo Jézéquel},
journal= {arXiv preprint arXiv:2201.02100},
year = {2024}
}
Comments
v2: added Propositions 2.6 and 2.7 and Appendix B v3: Electronic copy of final peer-reviewed manuscript accepted for publication