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, as put forth in Villani (2019). With the aim of achieving such a unification program, in this paper we initiate the study of gauge metric measure spaces.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Advanced Differential Geometry Research
Therapeutic Uses of Natural Elements
Publication details
- Journal / source
- Memoirs of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 317
- Issue
- 1613
- Publication date
- 9 February 2026
- Language
- EN