On the Brunn-Minkovski inequality and sub-Riemannian curvature

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-Émery curvature and the corresponding comparison theorems for distortion coefficients. The model spaces for comparison are variational problems coming from optimal control theory.

mathematical physicsanalysis of PDEsdifferential geometryspectral theory

Audience: researchers in the discipline

Analysis and Differential Geometry International Seminar @ Aveiro

Series comments: The online seminar Analysis and Differential Geometry International Seminar (ADGIS@Aveiro) aims to bring together specialists from analysis and geometry with particular emphasis on partial differential equations, differential geometry, analysis on filtered manifolds, singular (differential) operators, spectral theory, and their connections to other fields.

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