Local mollification of Riemannian metrics using Ricci flow, and Ricci limit spaces

Abstract

We use Ricci flow to obtain a local bi-Holder correspondence between Ricci limit spaces in three dimensions and smooth manifolds. This is more than a complete resolution of the three-dimensional case of the conjecture of Anderson-Cheeger-Colding-Tian, describing how Ricci limit spaces in three dimensions must be homeomorphic to manifolds, and we obtain this in the most general, locally non-collapsed case. The proofs build on results and ideas from recent papers of Hochard and the current authors.