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


Publication details

All authors or editorsIlmavirta, Joonas; Mönkkönen, Keijo

Journal or seriesJournal of Geometric Analysis

ISSN1050-6926

eISSN1559-002X

Publication year2023

Publication date24/02/2023

Volume33

Issue number4

Article number137

PublisherSpringer Science and Business Media LLC

Publication countryUnited States

Publication languageEnglish

DOIhttps://doi.org/10.1007/s12220-022-01182-w

Publication open accessOpenly available

Publication channel open accessPartially open access channel

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

Publication is parallel publishedhttps://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.


Keywordsdifferential geometryinverse problems

Free keywordsinverse problems; geodesic ray transform; integral geometry


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Ministry reportingYes

Reporting Year2023

Preliminary JUFO rating2


Last updated on 2024-03-04 at 18:16