6533b85efe1ef96bd12bf415

RESEARCH PRODUCT

Broken ray transform on a Riemann surface with a convex obstacle

Joonas IlmavirtaMikko Salo

subject

Statistics and ProbabilityMathematics - Differential GeometryGeodesicAstrophysics::High Energy Astrophysical PhenomenaBoundary (topology)Curvature01 natural sciencessymbols.namesakeMathematics - Analysis of PDEsFOS: Mathematics0101 mathematicsMathematicsRiemann surface010102 general mathematicsMathematical analysista111Regular polygonSurface (topology)boundary010101 applied mathematicsDifferential Geometry (math.DG)Obstaclesymbolstensor tomographyGeometry and TopologyStatistics Probability and UncertaintydimensionsConvex functionAnalysisAnalysis of PDEs (math.AP)

description

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.

yearjournalcountryeditionlanguage
2014-03-20
http://urn.fi/URN:NBN:fi:jyu-201611184670