Scattering rigidity for analytic metrics
| Autor: | Yannick Guedes Bonthonneau, Colin Guillarmou, Malo Jézéquel |
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| Přispěvatelé: | Université Sorbonne Paris Nord, Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, United States, European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 787304), European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 725967), PRC grant ADYCT (ANR-20-CE40-0017), ANR-20-CE40-0017,ADYCT,Aléatoire, dynamique et spectre(2020), European Project: 725967,IPFLOW, European Project: 787304,SOS, Jézéquel, Malo, Aléatoire, dynamique et spectre - - ADYCT2020 - ANR-20-CE40-0017 - AAPG2020 - VALID, Inverse Problems and Flows - IPFLOW - 725967 - INCOMING, Smooth dynamics via Operators, with Singularities - SOS - 787304 - INCOMING |
| Rok vydání: | 2022 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics - Analysis of PDEs Differential Geometry (math.DG) 37D20 37D40 35R30 FOS: Mathematics [MATH] Mathematics [math] Mathematics::Differential Geometry Dynamical Systems (math.DS) [MATH]Mathematics [math] Mathematics - Dynamical Systems Analysis of PDEs (math.AP) |
| Zdroj: | HAL |
| DOI: | 10.48550/arxiv.2201.02100 |
| Popis: | 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. Comment: v2: added Propositions 2.6 and 2.7 and Appendix B |
| Databáze: | OpenAIRE |
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