# On the Brunn-Minkovski inequality and sub-Riemannian curvature

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Davide Barilari
(UniversitÃ degli Studi di Padova)

created by beschastnyi on 05 Apr 2021

13 apr 2021
-- 17:00
[open in google calendar]

Aveiro

This is a part of the ADGIS @ Aveiro seminar. If you wish to attend the seminar write to i.beschastnyi@gmail.com

**Abstract.**

The classical Brunn-Minkovski inequality in the Euclidean space generalizes to Riemannian manifolds with Ricci curvature bounded from below. Indeed this inequality can be used to define the notion of "Ricci curvature bounded from below" for more general metric spaces. A class of spaces which do not satisfy this more general definition is the one of sub-Riemannian manifolds: these can be seen as a limit of Riemannian manifolds having Ricci curvature that is unbounded, whose prototype is the Heisenberg group.

In the first part of the talk I will discuss about the validity of a Brunn-Minkovsky type inequality in the SR setting. The second part concerns a notion of sub-Riemannian Bakry-Ã‰mery curvature and the corresponding comparison theorems for distortion coefficients. The model spaces for comparison are variational problems coming from optimal control theory.