Louis Yudowitz: Perelman Functionals for a Class of Intrinsic Geometric Flows

Much of Perelman's seminal work in Ricci flow relied on introducing various functionals (entropy, reduced length/distance, reduced volume) which are monotonic along the flow. This allowed, for instance, the proof of his celebrated no local collapsing theorem. These functionals and results have remained foundational to work in Ricci flow, but it is tempting to ask if these phenomena hold for a more general class of intrinsic geometric flows. In this talk we will present such a class of flows, which evolve the metric proportionally to a symmetric 2-tensor which satisfies a certain differential inequality. Some concrete cases will also be discussed, as well as some results that can be generalized from Ricci flow to this more general setting.