In this talk  we  examine  the Ricci flow of initial metric spaces  which are Reifenberg and locally 

bi-Lipschitz to Euclidean space. We show that any two    solutions   starting from such an initial metric space,    whose  Ricci curvatures are uniformly bounded from below and whose curvatures are bounded by $c\cdot t^{-1}$,     are  exponentially  in time  close to one another 

in the appropriate gauge. 

As an application, we show   that smooth three dimensional, 
complete, uniformly Ricci-pinched Riemannian manifolds with bounded curvature are either compact or flat, thus confirming a conjecture of Hamilton and Lott.