Producing 3D Ricci flows with nonnegative Ricci curvature via singular Ricci flows

Abstract

We extend the concept of singular Ricci flow by Kleiner and Lott from 3D compact manifolds to 3D complete manifolds with possibly unbounded curvature. As an application of the generalized singular Ricci flow, we show that for any 3D complete Riemannian manifold with nonnegative Ricci curvature, there exists a smooth Ricci flow starting from it. This partially confirms a conjecture by Topping.