Gradient flows, heat equation, and Brownian motion on time-dependent metric measure spaces

Karl-Theodor Sturm
Wednesday, February 15, 2017 - 5:00pm
TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Raum MA 004

We study the heat equation on time-dependent metric measure spaces (being a dynamic forward gradient flow for the energy) and its dual (being a dynamic backward gradient flow for the Boltzmann entropy). Monotonicity estimates for transportation distances and for squared gradients will be shown to be equivalent to the so-called dynamical convexity of the Boltzmann entropy on the Wasserstein space.