The preservation of product structures under the Ricci flow

In this talk, we show that if g(t) is a solution to the Ricci flow satisfying a certain non-uniform curvature bound and g(0) splits as a product, then the solution splits as a product for all time. The problem is framed as one of uniqueness for a related system to which we apply a maximum principle, in which the persistence of the product structure is encoded in time-dependent projections.