Geodesic
X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds
[Transformée en rayons X et rigidité du bord pour les variétés asymptotiquement hyperboliques]
Graham, C. Robin1 ; Guillarmou, Colin2 ; Stefanov, Plamen3 ; Uhlmann, Gunther4
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
Annales de l'Institut Fourier, Riemannian Geometry. Past, Present and Future an homage to Marcel Berger December 6–9, 2017, IHES, Bures-sur-Yvette, Tome 69 (2019) no. 7, pp. 2857-2919 Cet article a éte moissonné depuis la source Numdam

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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.

Publié le :
DOI : 10.5802/aif.3339
Classification : 35R30, 37D40, 53C22
Keywords: X-ray transform, boundary rigidity, asymptotically hyperbolic manifold
Mots-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
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {X-Ray {Transform} and {Boundary} {Rigidity} for {Asymptotically} {Hyperbolic} {Manifolds}},
     journal = {Annales de l'Institut Fourier},
     pages = {2857--2919},
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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, Tome 69 (2019) no. 7, pp. 2857-2919. doi: 10.5802/aif.3339

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