Calculus of Variations and Geometric Measure Theory

The low temperature limit of Dirichlet energies

Mauro Mariani

created by novaga on 08 Dec 2018

17 dec 2018 -- 10:30   [open in google calendar]

Aula Marie Curie, Scuola Normale Superiore


Let $M$ be a Riemannian manifold equipped with a reference measure $m$ with density $\exp(- V/T)$ with respect to the volume measure, where $V$ represents a potential and the positive constant $T$ represents the temperature. The Dirichlet energy with reference measure m is a classical functional defined on the space of probability measures on $M$. I will discuss the variational convergence of such a functional in the limit $T \to 0$. In particular, if $V$ is not convex, a non-trivial expansion by $\Gamma$-convergence holds under generic hypotheses on $V$. The results are based on a joint work with G. DiGesu (TU Wien).