A note on Ricci flow with Ricci curvature bounded below

In this note, we will prove that given a sequence of Ricci flows (M_k, g_k(t)) of dimension n, t ∈ [-1, 0], with Ricci curvature bounded below uniformly and volume noncollapsing, (M_k, g_k(0)) converge as a sequence of manifolds to a limit length space (X, d). The regular part of (X, d) must be open and the convergence is of C^1,α regularity. As a corollary of this result, we prove that in dimension 3, a Ricci flow can always extend unless either its Ricci curvature goes to -∞ or it shrinks to a point.