Topics in Optimal Transportation

2003/03/25 by Cédric Villani · 59 citations
Computer Science · Mathematics · Engineering · #Optimization and Variational Analysis #Point processes and geometric inequalities #Computer science #Business #Transport engineering #Engineering

paper · doi:10.1090/gsm/058

openalex publication_date 2003/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

Introduction The Kantorovich duality Geometry of optimal transportation Brenier's polar factorization theorem The Monge-Ampere equation Displacement interpolation and displacement convexity Geometric and Gaussian inequalities The metric side of optimal transportation A differential point of view on optimal transportation Entropy production and transportation inequalities Problems Bibliography Table of short statements Index.

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