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

Davide Barilari (1) , Andrea Mondino (2) , Luca Rizzi (3, 4)

1 Unipd - Università degli Studi di Padova = University of Padua
2 University of Oxford
3 IF - Institut Fourier
4 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies

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.

Domaines: Optimisation et contrôle [math.OC]; Géométrie métrique [math.MG]; Géométrie différentielle [math.DG]

Davide Barilari, Andrea Mondino, Luca Rizzi. Unified synthetic Ricci curvature lower bounds for Riemannian and sub-Riemannian structures. 2022. ⟨hal-03856993⟩