Calculus of Variations and Geometric Measure Theory

D. Barilari - A. Mondino - L. Rizzi

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

created by rizzi1 on 17 Nov 2022
modified on 14 Mar 2024


Accepted Paper

Inserted: 17 nov 2022
Last Updated: 14 mar 2024

Journal: Memoirs of the AMS
Year: 2024

ArXiv: 2211.07762 PDF


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.