Boundary and lens rigidity for non-convex manifolds

  title={Boundary and lens rigidity for non-convex manifolds},
  author={Colin Guillarmou and Marco Mazzucchelli and Leo Tzou},
  journal={arXiv: Differential Geometry},
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… 

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