Zoltán Balogh (University of Bern): Logarithmic Sobolev Inequality on Surfaces via OMT

In the first part of  this talk I present a proof of the Logarithmic Sobolov Inequality (LSI) in the Euclidean space,  that is based on the method of optimal mass transport (OMT). In the second part of the talk I show, that this method is strong enough to obtain a version of the LSI in curved spaces such as  Euclidean surfaces. In this case the statement of the LSI  involves the mean curvature of the surface.

The talk is based on a joint work with Alexandru Kristaly.