Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures

2022/11/14 by Barilari, Davide, Mondino, Andrea, Rizzi, Luca · 1 citation
#49Q22 #53C17 #53C21 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2211.07762

Abstract

Recent advances in the theory of metric measures spaces on the one hand, and of sub-Riemannian ones on the other hand, suggest the possibility of a "great unification" of Riemannian and sub-Riemannian geometries in a comprehensive framework of synthetic Ricci curvature lower bounds. With the aim of achieving such a unification program, in this paper we initiate the study of gauge metric measure spaces.

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• Universal non-CD of sub-Riemannian manifolds

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