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

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.

arXiv comment153 pages. v2: new Section 10.2 on the Grushin plane. v3: minor cosmetic changes. Accepted version, to appear on Memoirs of the AMS

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