Optimal maps and local-to-global property in negative dimensional spaces with Ricci curvature bounded from below

2021/05/25 by Magnabosco, Mattia, Rigoni, Chiara
#Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2105.12017

Abstract

In this paper we investigate two important properties of metric measure spaces satisfying the reduced curvature-dimension condition for negative values of the dimension parameter: the existence of a transport map between two suitable marginals and the so-called local-to-global property.

Related

• Optimal transport and Ricci curvature for metric-measure spaces
• Local curvature-dimension condition implies measure-contraction property
• Existence and uniqueness of optimal transport maps
• Ricci curvature for metric-measure spaces via optimal transport
• Ricci curvature, entropy and optimal transport