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Dynamics, Geometry and Groups Seminar

Speaker: Liangbing (Luo)

Title: Logarithmic Sobolev inequalities on sub-Riemannian manifolds

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. As for many of sub-Riemannian manifolds, curvature bounds (or classical Bakry-Emery estimates) are not available. We use different techniques, such as symmetry of the space, to study the inequality and its constant, especially its dimension-free property. Examples in both finite and infinite dimensional settings are provided.