  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.
