A1 Journal article (refereed)
The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds (2023)

Ilmavirta, J., & Mönkkönen, K. (2023). The Geodesic Ray Transform on Spherically Symmetric Reversible Finsler Manifolds. Journal of Geometric Analysis, 33(4), Article 137. https://doi.org/10.1007/s12220-022-01182-w

JYU authors or editors

Ilmavirta, Joonas
Mönkkönen, Keijo

Publication details

All authors or editors: Ilmavirta, Joonas; Mönkkönen, Keijo

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2023

Publication date: 24/02/2023

Volume: 33

Issue number: 4

Article number: 137

Publisher: Springer Science and Business Media LLC

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-022-01182-w

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85756

Publication is parallel published: https://arxiv.org/abs/2203.16886

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.

Keywords: differential geometry; inverse problems

Free keywords: inverse problems; geodesic ray transform; integral geometry

Fields of science: