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

Department's Seminar
16 May 2023
Start time 
2:30 pm
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room "1"
Target audience: 
University community
UniTrento students
Contact person: 
Andrea Pinamonti, Andrea Marchese, Giorgio Saracco, Gian Paolo Leonardi
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
Davide Barilari (University of Padua)


The Lott-Sturm-Villani theory of CD(K, N) metric measure spaces satisfying Ricci curvature lower bounds in a synthetic sense via optimal transport, though extremely successful, has been shown not to directly apply to sub-Riemannian geometries. Nonetheless, still using optimal transport tools, some entropy inequalities have been proved to hold in the case of the Heisenberg group and more in general in sub-Riemannian manifolds.
In this talk we survey the known results and motivate a new approach we propose aiming to unify Riemannian and sub-Riemannian synthetic Ricci lower bounds, introducing suitable curvature dimension conditions. A main novelty is that we consider metric measure spaces endowed with a gauge function, and we allow general distortion coefficients. 
The talk is based on a joint work with Andrea Mondino (Oxford) and Luca Rizzi (SISSA).

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