Boundary and lens rigidity for non-convex manifolds

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.

40 pages, 2 figures

Cited by in corpus (4)

• Inverse problems for nonlinear magnetic Schrödinger equations on conformally transversally anisotropic manifolds
• Remarks on the anisotropic Calderón problem
• On the number of poles of the dynamical zeta functions for billiard flow
• Calderón problem for fractional Schrödinger operators on closed Riemannian manifolds