Some Remarks on Transportation Cost and Related Inequalities

2004/05/31 by Mark W. Meckes · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.FA #math.MG #math.PR #msc:52A20 #msc:60E15

paper · pdf · doi:10.1007/978-3-540-72053-9_12

published as Geometric Aspects of Functional Analysis, 237-244, Lecture Notes in Math. 1910, Springer, Berlin, 2007. · AMSLaTeX; v3: version to appear in GAFA Israel Seminar notes

arxiv created 2005/08/09 · openalex publication_date 2007/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We discuss transportation cost inequalities for uniform measures on convex bodies, and connections with other geometric and functional inequalities. In particular, we show how transportation inequalities can be applied to the slicing problem, and give a new log-Sobolev-type inequality for bounded domains in Rⁿ.

Citations

• Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality

Cited by

• Optimal Transport