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.
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
@article{AIF_2019__69_7_2857_0, author = {Graham, C. Robin and Guillarmou, Colin and Stefanov, Plamen and Uhlmann, Gunther}, title = {X-Ray {Transform} and {Boundary} {Rigidity} for {Asymptotically} {Hyperbolic} {Manifolds}}, journal = {Annales de l'Institut Fourier}, pages = {2857--2919}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {69}, number = {7}, year = {2019}, doi = {10.5802/aif.3339}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3339/} }
TY - JOUR AU - Graham, C. Robin AU - Guillarmou, Colin AU - Stefanov, Plamen AU - Uhlmann, Gunther TI - X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds JO - Annales de l'Institut Fourier PY - 2019 SP - 2857 EP - 2919 VL - 69 IS - 7 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3339/ DO - 10.5802/aif.3339 LA - en ID - AIF_2019__69_7_2857_0 ER -
%0 Journal Article %A Graham, C. Robin %A Guillarmou, Colin %A Stefanov, Plamen %A Uhlmann, Gunther %T X-Ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds %J Annales de l'Institut Fourier %D 2019 %P 2857-2919 %V 69 %N 7 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3339/ %R 10.5802/aif.3339 %G en %F AIF_2019__69_7_2857_0
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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