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arXiv · 1711.10059

Boundary and lens rigidity for non-convex manifolds

Colin Guillarmou·Marco Mazzucchelli·Leo Tzou
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Abstract

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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Colin Guillarmou, Marco Mazzucchelli, Leo Tzou. 2017-11-28. Boundary and lens rigidity for non-convex manifolds. https://doi.org/10.1353/ajm.2021.0012

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