Logarithmic Sobolev inequalities on sub-Riemannian manifolds
Liangbing Luo, Queen's University
Abstract: The logarithmic Sobolev inequality has been first introduced and studied by L. Gross on a Euclidean space, and since then it found many applications. In particular, many existing results concern the question on how the constant in the logarithmic Sobolev inequality depends on the geometry of the underlying space. In this talk, I will review recent results on the study of the constant (and its dimension-independence) in the logarithmic Sobolev inequality on sub-Riemannian manifolds. As for many of such setting curvature bounds (or classical Bakry-Emery estimates) are not available, we use different techniques. Examples in both finite and infinite dimensional settings are provided.
