Curvature-dimension inequalities and Li-Yau inequalities in sub-Riemannian spaces

TL;DR

This paper surveys the development of curvature-dimension inequalities and Li-Yau inequalities within sub-Riemannian spaces, highlighting a collaborative research program and its key advancements.

Contribution

It consolidates and reviews a series of works on curvature-dimension and Li-Yau inequalities in sub-Riemannian geometry, emphasizing collaborative progress.

Findings

Development of curvature-dimension inequalities in sub-Riemannian spaces

Establishment of Li-Yau inequalities in this geometric setting

Progress in understanding geometric analysis in sub-Riemannian contexts

Abstract

In this paper we present a survey of the joint program with Fabrice Baudoin originated with the paper \cite{BG1}, and continued with the works \cite{BG2}, \cite{BBG}, \cite{BG3} and \cite{BBGM}, joint with Baudoin, Michel Bonnefont and Isidro Munive.