Broken ray transform on a Riemann surface with a convex obstacle

Broken Ray Transform on a Riemann Surface with a Convex Obstacle

We consider the broken ray transform on Riemann surfaces in the presence of an obstacle. 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 ra...

Inversion formulas for the broken-ray Radon transform

The inverse transport problem consists of recovering the spatially varying absorption and scattering coefficients of the interior of a highly scattering medium from measurements taken on its boundary [2]. The problem has been widely studied in the context of optical tomography (OT)—a biomedical imaging modality that makes use of multiply-scattered light to visualize structural variations in the...

Counting Ovals on a Symmetric Riemann Surface

Let S be a compact Riemann surface without boundary. A symmetry of S is an anti-conformal, involutary automorphism. The xed point set of is a disjoint union of circles, each of which is called an oval of . A method is presented for counting the ovals of a symmetry when S admits a large group G of automorphisms, normalized by . The method involves only calculations in G, based on the geometric d...

Projective Structures on a Riemann Surface *

Some Kernels on a Riemann Surface

We discuss certain kernels on a Riemann surface constructed mainly via BakerAkhiezer (BA) functions and indicate relations to dispersionless theory.