Abstract:

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 which in turn is the defining property of super-Ricci flows of

metric measure spaces.

海报