Geodesic X-ray tomography for piecewise constant functions on nontrapping manifolds

2017/02/24 by Ilmavirta, Joonas, Lehtonen, Jere, Salo, Mikko · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.07622

Abstract

We show that on a two-dimensional compact nontrapping manifold with strictly convex boundary, a piecewise constant function is determined by its integrals over geodesics. In higher dimensions, we obtain a similar result if the manifold satisfies a foliation condition. These theorems are based on iterating a local uniqueness result. Our proofs are elementary.

Cited by

• A family of non-simple surfaces whose transport twistor spaces admit global blow-down maps
• The matrix weighted real-analytic double fibration transforms

Related

• Geodesic tomography problems on Riemannian manifolds
• Pestov identities and X-ray tomography on manifolds of low regularity
• Integral geometry on manifolds with boundary and applications
• On the microlocal analysis of the geodesic X-ray transform with conjugate points
• Geodesic X-ray transform and streaking artifacts on simple surfaces or on spaces of constant curvature