Cambridge Journal of Mathematics

Volume 12 (2024)

Number 1

Scattering rigidity for analytic metrics

Pages: 165 – 222

DOI: https://dx.doi.org/10.4310/CJM.2024.v12.n1.a2

Authors

Yannick Guedes-Bonthonneau (Université Paris-Nord, CNRS, LAGA, Villetaneuse, France)

Colin Guillarmou (Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, Orsay, France)

Malo Jézéquel (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)

Abstract

For analytic negatively curved Riemannian manifolds 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 set assumptions.

Received 14 April 2022

Published 30 January 2024