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Local lens rigidity
for manifolds of Anosov type
Mihajlo Cekić, Colin Guillarmou and Thibault Lefeuvre |
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Vol. 17 (2024), No. 8, 2737–2795
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Abstract |
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The lens data of a Riemannian manifold with boundary is the collection of lengths of geodesics with endpoints on the boundary, together with their incoming and outgoing vectors. We show that negatively curved Riemannian manifolds with strictly convex boundary are locally lens rigid in the following sense: if is such a metric, then any metric sufficiently close to and with the same lens data is isometric to , up to a boundary-preserving diffeomorphism. More generally, we consider the same problem for a wider class of metrics with strictly convex boundary, called metrics of Anosov type. We prove that the same rigidity result holds within that class in dimension and in any dimension, further assuming that the curvature is nonpositive. |
Keywords
lens data, lens rigidity, microlocal analysis, hyperbolic
dynamics, anisotropic spaces, inverse problems, resolvent,
X-ray transform
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Mathematical Subject Classification
Primary: 35R30, 53C24
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Milestones
Received: 11 May 2022
Revised: 22 May 2023
Accepted: 18 July 2023
Published: 12 October 2024
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Authors |
| Mihajlo Cekić | |
| Institut für Mathematik Universität Zürich Zürich Switzerland |
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| Colin Guillarmou | |
| Laboratoire de Mathematiques
d’Orsay CNRS, Université Paris-Saclay Orsay France |
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| Thibault Lefeuvre | |
| Institut de Mathématiques de
Jussieu-Paris Rive Gauche Sorbonne Université Campus Pierre et Marie Curie Paris France |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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