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Article Dans Une Revue American Journal of Mathematics Année : 2021

Boundary and lens rigidity for non-convex manifolds

Résumé

We study the boundary and lens rigidity problems on domains without assuming the convexity of the boundary. We show that such rigidities hold when the domain is a simply connected compact Riemannian surface without conjugate points. For the more general class of non-trapping compact Riemannian surfaces with no conjugate points, we show lens rigidity. We also prove the injectivity of the X-ray transform on tensors in a variety of settings with non-convex boundary and, in some situations, allowing a non-empty trapped set.
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Dates et versions

hal-01827894 , version 1 (02-07-2018)

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Colin Guillarmou, Marco Mazzucchelli, Leo Tzou. Boundary and lens rigidity for non-convex manifolds. American Journal of Mathematics, 2021, 143 (2), pp.533-575. ⟨10.1353/ajm.2021.0012⟩. ⟨hal-01827894⟩
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