Scattering rigidity for analytic metrics

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 categ...

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Bibliographic Details
Published in:arXiv.org 2024-02
Main Authors: Yannick Guedes Bonthonneau, Guillarmou, Colin, Malo Jézéquel
Format: Article
Language:English
Subjects:
Conjugate points
Flow mapping
Mathematical analysis
Riemann manifold
Scattering
Topology
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2201.02100