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The X-ray transform on Anosov manifolds Lefeuvre, Thibault
Description
A closed Riemannian manifold is said to be Anosov if its geodesic flow on its unit tangent bundle is Anosov (also called uniformly hyperbolic in the literature). Typical examples are provided by negatively-curved manifolds. On such manifolds, the X-ray transform is simply defined as the integration of continuous functions along periodic geodesics. I will review some recent results on the analytic study of the X-ray transform (in particular, stability estimates). The techniques rely on microlocal tools introduced by Guillarmou and further investigated by Guillarmou-Lefeuvre, and on new finite and approximate Livsic theorems proved by Gouëzel-Lefeuvre. If time permits, I will explain how these results can be applied to prove the local rigidity of the marked length spectrum.
Item Metadata
Title |
The X-ray transform on Anosov manifolds
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-04-15T16:20
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Description |
A closed Riemannian manifold is said to be Anosov if its geodesic flow on its unit tangent bundle is Anosov (also called uniformly hyperbolic in the literature). Typical examples are provided by negatively-curved manifolds. On such manifolds, the X-ray transform is simply defined as the integration of continuous functions along periodic geodesics. I will review some recent results on the analytic study of the X-ray transform (in particular, stability estimates). The techniques rely on microlocal tools introduced by Guillarmou and further investigated by Guillarmou-Lefeuvre, and on new finite and approximate Livsic theorems proved by Gouëzel-Lefeuvre. If time permits, I will explain how these results can be applied to prove the local rigidity of the marked length spectrum.
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Extent |
43.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Université d’Orsay
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Series | |
Date Available |
2019-10-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0383382
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International