The partial data Calder\'on problem in dimension three

We consider an inverse boundary value problem for the time-independent Schr\"odinger equation in dimension three. We prove that the local Dirichlet-to-Neumann map defined near a boundary point uniquely determines the potential in a neighborhood of the boundary point in the interior. In particular, we show that the uniqueness question can be reduced to the injectivity of a weighted X-ray transform, which links inverse boundary value problems to integral geometry.