Titre :

Computing the cut locus of a Riemannian manifold via optimal transport

Auteur(s) :

Facca, Enrico [Auteur correspondant]
Reliable numerical approximations of dissipative systems [RAPSODI]
Berti, Luca [Auteur]
Institut de Recherche Mathématique Avancée [IRMA]
Fassò, Francesco [Auteur]
Dipartimento di Matematica [Padova]
Putti, Mario [Auteur]
Dipartimento di Matematica [Padova]

Titre de la revue :

ESAIM: Mathematical Modelling and Numerical Analysis

Pagination :

1939-1954

Éditeur :

Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP

Date de publication :

2022-11

ISSN :

2822-7840

Mot(s)-clé(s) en anglais :

Cut locus
Riemannian geometry
Optimal Transport problem
Monge–Kantorovich equations
geodesic distance

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

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 ...
Lire la suite >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 ℝ3, and discuss advantages and limitations.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL