Pestov identities and X-ray tomography on manifolds of low regularity

2021/12/10 by Joonas Ilmavirta, Antti Kykkänen, Ilmavirta, Joonas +1 · 1 citation
Mathematics · Medicine · #44A12 #53C22 #53C65 #58J32 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Medical Imaging Techniques and Applications #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2112.05523

openalex publication_date 2021/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the geodesic X-ray transform is injective on scalar functions and (solenoidally) on one-forms on simple Riemannian manifolds (M,g) with g ∈ C^1,1. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This C^1,1-regularity is optimal on the Hölder scale. The bulk of the article is devoted to setting up a calculus of differential and curvature operators on the unit sphere bundle atop this non-smooth structure.

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