X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds
Annales de l'Institut Fourier, Riemannian Geometry. Past, Present and Future an homage to Marcel Berger December 6–9, 2017, IHES, Bures-sur-Yvette, Volume 69 (2019) no. 7, pp. 2857-2919.

We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary measurements for the geodesic flow.

On considère le problème de rigidité du bord pour les variétés asymptotiquement hyperboliques. Nous montrons l’injectivité de la transformée en rayons X dans plusieurs cas et considérons le problème inverse non-linéaire qui consiste en la détermination de la métrique à partir de données au bord sur le flot géodésique.

Published online:
DOI: 10.5802/aif.3339
Classification: 35R30, 37D40, 53C22
Keywords: X-ray transform, boundary rigidity, asymptotically hyperbolic manifold
Mot clés : transformée en rayons X, rigidité du bord, variété asymptotiquement hyperbolique

Graham, C. Robin 1; Guillarmou, Colin 2; Stefanov, Plamen 3; Uhlmann, Gunther 4

1 Department of Mathematics University of Washington Box 354350 Seattle, WA 98195-4350 (USA)
2 Laboratoire de Mathématiques d’Orsay UMR 8628 du CNRS, Université Paris-Sud 91405 Orsay Cedex (France)
3 Department of Mathematics Purdue University West Lafayette, IN 47907 (USA)
4 Department of Mathematics University of Washington Seattle, WA 98195-4350 (USA) and Institute for Advanced Study of the HKUST Hong Kong University of Science and Technology Clear Water Bay, New Territories, Hong Kong
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Graham, C. Robin; Guillarmou, Colin; Stefanov, Plamen; Uhlmann, Gunther. X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds. Annales de l'Institut Fourier, Riemannian Geometry. Past, Present and Future an homage to Marcel Berger December 6–9, 2017, IHES, Bures-sur-Yvette, Volume 69 (2019) no. 7, pp. 2857-2919. doi : 10.5802/aif.3339. https://aif.centre-mersenne.org/articles/10.5802/aif.3339/

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