Pestov identities and X-ray tomography on manifolds of low regularity
Pestov identities and X-ray tomography on manifolds of low regularity
We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds $ (M,g) $ with $ g \in C^{1,1} $. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This $ C^{1,1} $-regularity …