Ricci curvature on polyhedral surfaces via optimal transportation - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Axioms Année : 2014

Ricci curvature on polyhedral surfaces via optimal transportation

Résumé

The problem of defining correctly geometric objects such as the curvature is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs. He named it coarse Ricci curvature because it coincides, up to some given factor, with the classical Ricci curvature, when the space is a smooth manifold. Lin, Lu & Yau, Jost & Liu have used and extended this notion for graphs giving estimates for the curvature and hence the diameter, in terms of the combinatorics. In this paper, we describe a method for computing the coarse Ricci curvature and give sharper results, in the specific but crucial case of polyhedral surfaces.
Fichier principal
Vignette du fichier
Ricci_Curvature_on_Polyhedral_Surfaces_via_Optimal_Transportation.pdf (291.28 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-00941486 , version 1 (03-02-2014)
hal-00941486 , version 2 (11-03-2014)

Identifiants

Citer

Benoît Loisel, Pascal Romon. Ricci curvature on polyhedral surfaces via optimal transportation. Axioms, 2014, 3 (1), pp.119-139. ⟨10.3390/axioms3010119⟩. ⟨hal-00941486v2⟩
240 Consultations
306 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More