Logarithmic Sobolev Inequalities on Homogeneous Spaces

Explore a 48-minute lecture on logarithmic Sobolev inequalities in homogeneous spaces presented by Langbing Luo from UConn. Delve into the study of sub-Riemannian manifolds as homogeneous spaces with structures induced by transitive Lie group actions. Examine the properties of sub-Laplacians as hypoelliptic operators and investigate logarithmic Sobolev inequalities in this context. Learn how the logarithmic Sobolev constant depends on the acting Lie group but remains independent of its isotropy group's action. Discover insights into the relationship between the logarithmic Sobolev constant and the geometry of the underlying space, including its independence from dimension in several examples. Gain understanding of this research based on joint work with M. Gordina, presented at the Institut des Hautes Etudes Scientifiques (IHES).