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• W3172335523 abstract "In this paper, we give a new characterization of the cut locus of a point on a compact Riemannian manifold as the zero set of the optimal transport density solution of the Monge–Kantorovich equations, a PDE formulation of the optimal transport problem with cost equal to the geodesic distance. Combining this result with an optimal transport numerical solver, based on the so-called dynamical Monge–Kantorovich approach, we propose a novel framework for the numerical approximation of the cut locus of a point in a manifold. We show the applicability of the proposed method on a few examples settled on 2d-surfaces embedded in ℝ 3 , and discuss advantages and limitations." @default.
• W3172335523 created "2021-06-22" @default.
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• W3172335523 date "2022-11-01" @default.
• W3172335523 modified "2023-10-16" @default.
• W3172335523 title "Computing the cut locus of a Riemannian manifold via optimal transport" @default.
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• W3172335523 doi "https://doi.org/10.1051/m2an/2022059" @default.
• W3172335523 hasPublicationYear "2022" @default.
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