On the extension conditions for Ricci flow

Let {(Mn, g(t)), 0 ≤ t < T < infinity} be an unnormalized Ricci flow solution: 6gij6t = -2Rij for t ∈ [0, T). Richard Hamilton showed that if the Riemannian curvature is uniformly bounded on the spacetime Mn x [0, T), then the solution can be extended over T . Natasa Sesum proved that a uniform bound of Ricci curvature is enough to extend the flow. We show that if Ricci curvature is bounded from below, then scalar curvature's Ln+22 norm (over spacetime) bound is enough to extend the flow. Moreover, the constant n+22 is optimal.