Pestov identities and X-ray tomography on manifolds of low regularity
Ilmavirta, J., & Kykkänen, A. (2023). Pestov identities and X-ray tomography on manifolds of low regularity. Inverse Problems and Imaging, 17(6), 1301-1328. https://doi.org/10.3934/ipi.2023017
Published inInverse Problems and Imaging
DisciplineMatematiikkaInversio-ongelmien huippuyksikköMathematicsCentre of Excellence in Inverse Problems
© 2023 American Institute of Mathematical Sciences (AIMS)
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 ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity that is compatible with rough geometry. This C1,1-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.
PublisherAmerican Institute of Mathematical Sciences (AIMS)
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Research Fellow, AoF
Additional information about fundingBoth authors were supported by the Academy of Finland (JI by grants 332890 and 351665, AK by 336254).
Showing items with similar title or keywords.
Ilmavirta, Joonas; Kykkänen, Antti (American Institute of Mathematical Sciences (AIMS), 2023)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 ∈ C1,1. In addition to a proof, we produce a redefinition of simplicity ...
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