Calculus of Variations and Geometric Measure Theory

Analysis and Geometry on Singular Spaces

Heat and entropy flows on metric measure spaces

Martin Kell

created by paolini on 25 Apr 2014
modified on 07 May 2014


In this talk I will show how to extend the calculus of the abstract heat flow developed by Ambrosio-Gigli-Savaré to construct an abstract $q$-heat flow as the gradient flow of the $q$-Cheeger energy. A sufficient condition for mass preservation and a calculus of functionals along this flow will be given. Having this, I will show that this abstract $q$-heat flow solves the gradient flow of the Renyi entropy in the p-Wasserstein space if the Renyi entropy is displacement convex. In case $1< p < 2$, it can be shown that this gradient flow is unique which implies that $q$-heat flow and the Renyi entropy flow can be identified.