Stable recovery of a simple irreversible Finsler geometry from travel time data (bibtex)

by Maarten V. de Hoop, Joonas Ilmavirta, Antti Kykkänen and Teemu Saksala

Abstract:

We show that a simple irreversible Finsler geometry can be recovered uniquely and Lipschitz-stably from its travel time data. We introduce and use a version of Gromov–Hausdorff distance adapted to irreversible metric spaces. In contrast to reversible (e.g. Riemannian) geometry, even the question of stability becomes ill-defined without simplicity.

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Reference:

Stable recovery of a simple irreversible Finsler geometry from travel time data (Maarten V. de Hoop, Joonas Ilmavirta, Antti Kykkänen and Teemu Saksala), 2026. [show abstract] [hide abstract] We show that a simple irreversible Finsler geometry can be recovered uniquely and Lipschitz-stably from its travel time data. We introduce and use a version of Gromov–Hausdorff distance adapted to irreversible metric spaces. In contrast to reversible (e.g. Riemannian) geometry, even the question of stability becomes ill-defined without simplicity. [arXiv]

Bibtex Entry:

@unpublished{stable-irreversible-finsler,
    author = {Maarten V. de Hoop and Joonas Ilmavirta and Antti Kykk\"{a}nen and Teemu Saksala},
    title = {{Stable recovery of a simple irreversible Finsler geometry from travel time data}},
    month = jun,
    year = 2026,
    arxiv = {2606.25138},
    url = {http://users.jyu.fi/~jojapeil/pub/stable-irreversible-finsler.pdf},
    abstract = {We show that a simple irreversible Finsler geometry can be recovered uniquely and Lipschitz-stably from its travel time data. We introduce and use a version of Gromov--Hausdorff distance adapted to irreversible metric spaces. In contrast to reversible (e.g. Riemannian) geometry, even the question of stability becomes ill-defined without simplicity.}
}