Ricci Flow Under Kato-Type Curvature Lower Bound

Abstract

In this work, we extend the existence theory of non-collapsed Ricci flows from point-wise curvature lower bound to Kato-type curvature lower bound. As an application, we prove that any compact three-dimensional non-collapsed strong Kato limit space is homeomorphic to a smooth manifold. Moreover, similar result also holds in higher dimension under stronger curvature condition. We also use the Ricci flow smoothing to study stability problem in scalar curvature geometry.