  This paper investigates the question of stability for a class of Ricci flows
which start at possibly non-smooth metric spaces. We show that if the initial
metric space is Reifenberg and locally bi-Lipschitz to Euclidean space, then
two solutions to the Ricci flow whose Ricci curvature is uniformly bounded from
below and whose curvature is bounded by $c\cdot t^{-1}$ converge to one another
at an exponential rate once they have been appropriately gauged. 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.
