Continuity of optimal transport maps and convexity of injectivity domains on the two-sphere - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2009

Continuity of optimal transport maps and convexity of injectivity domains on the two-sphere

Résumé

Given a compact Riemannian manifold, we study the regularity of the optimal transport map between two probability measures with cost given by the squared Riemannian distance. Our strategy is to define a new form of the so-called Ma-Trudinger-Wang condition and to show that this condition, together with the strict convexity of the nonfocal domains, implies the continuity of the optimal transport map. Moreover our new condition, again combined with the strict convexity of the nonfocal domains, allows to prove that all injectivity domains are strictly convex too. These results apply for instance on any small C4 -deformation of the two-sphere.
Fichier principal
Vignette du fichier
MTWFigRifTCL_final.pdf (332.15 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00923261 , version 1 (02-01-2014)

Identifiants

  • HAL Id : hal-00923261 , version 1

Citer

Alessio Figalli, Ludovic Rifford. Continuity of optimal transport maps and convexity of injectivity domains on the two-sphere. Communications on Pure and Applied Mathematics, 2009, 62 (12), pp.1670. ⟨hal-00923261⟩
296 Consultations
96 Téléchargements

Partager

Gmail Facebook X LinkedIn More