Broken ray transform on a Riemann surface with a convex obstacle

摘要

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov [22]. If the surface has nonpositive curvature and the obstacle is strictly convex, we show that a function is determined by its integrals over broken geodesic rays that reflect on the boundary of the obstacle. Our proof is based on a Pestov identity with boundary terms, and it involves Jacobi fields on broken rays. We also discuss applications of the broken ray transform.