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arXiv · 2211.07762

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

Davide Barilari·Andrea Mondino·Luca Rizzi
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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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Davide Barilari, Andrea Mondino, Luca Rizzi. 2022-11-14. Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures. https://doi.org/10.1090/memo/1613

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