Communications in Analysis and Geometry

Volume 24 (2016)

Number 2

Broken ray transform on a Riemann surface with a convex obstacle

Pages: 379 – 408

DOI: http://dx.doi.org/10.4310/CAG.2016.v24.n2.a6

Authors

Joonas Ilmavirta (Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Mikko Salo (Department of Mathematics and Statistics, University of Jyväskylä, Finland)

Abstract

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle, following earlier work of Mukhometov. 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.

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Published 14 June 2016