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Séminaire Équations aux dérivées partielles (Polytechnique)

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Cédric Villani
Transport optimal et courbure de Ricci
Séminaire Équations aux dérivées partielles (Polytechnique) (2005-2006), Exp. No. 7, 18 p.
Article PDF | Reviews MR 2276073

Résumé - Abstract

Des liens inattendus ont été récemment mis à jour entre le transport optimal de Monge–Kantorovich et certains problèmes de géométrie riemannienne, en liaison avec la courbure de Ricci. Une des retombées de ces interactions est la naissance d’une théorie “synthétique” des espaces métriques mesurés à courbure de Ricci minorée, venant compléter la théorie classique des espaces métriqes à courbure sectionnelle minorée. Dans ce texte (également fourni aux actes du Séminaire de Théorie Spectrale et Géométrie de Grenoble), je passerai en revue ces développements de manière concise et informelle. Les notes bibliographiques renvoient à des sources plus complètes et précises.

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