Broken ray transform for twisted geodesics on surfaces with a reflecting obstacle
- Resource Type
- Working Paper
- Authors
- Jathar, Shubham R.; Kar, Manas; Railo, Jesse
- Source
- The Journal of Geometric Analysis 34, 212 (2024)
- Subject
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
Primary 44A12, Secondary 58C99, 37E35
- Language
We prove a uniqueness result for the broken ray transform acting on the sums of functions and $1$-forms on surfaces in the presence of an external force and a reflecting obstacle. We assume that the considered twisted geodesic flows have nonpositive curvature. The broken rays are generated from the twisted geodesic flows by the law of reflection on the boundary of a suitably convex obstacle. Our work generalizes recent results for the broken geodesic ray transform on surfaces to more general families of curves including the magnetic flows and Gaussian thermostats.
Comment: Accepted version of manuscript, 39 pages