Neumann heat flow and gradient flow for the entropy on Non-convex domains

In this talk we consider the gradient flow for the Boltzmann entropy on the Wasserstein space of probability measures supported on a subset of Euclidean space, Riemannian manifolds, or an RCD space. For a large class of non-convex smooth subsets, we show that the gradient flow for the Boltzmann entropy exists - despite the fact that the entropy is not semiconvex - and coincides with the heat flow with Neumann boundary conditions. This is joint work with K.-T. Sturm.