The geodesic ray transform on spherically symmetric reversible Finsler manifolds

2022/03/31 by Joonas Ilmavirta, Ilmavirta, Joonas, Keijo Mönkkönen +1 · 1 citation
Physics and Astronomy · #44A12 #53A99 #86A22 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2203.16886

openalex publication_date 2022/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the geodesic ray transform is injective on scalar functions on spherically symmetric reversible Finsler manifolds where the Finsler norm satisfies a Herglotz condition. We use angular Fourier series to reduce the injectivity problem to the invertibility of generalized Abel transforms and by Taylor expansions of geodesics we show that these Abel transforms are injective. Our result has applications in linearized boundary rigidity problem on Finsler manifolds and especially in linearized elastic travel time tomography.

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