Abstract

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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 533-575
Launched on MUSE
2021-03-16
Open Access
No
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