Curvature Estimates for the Ricci Flow II
  In this paper we present several curvature estimates and convergence results for solutions of the Ricci flow. The curvature estimates depend on smallness of certain local space-time integrals of the norm of the Riemann curvature tensor, while the convergence results require finiteness of space-time integrals of the norm of the Riemann curvature tensor. They also serve as characterizations of blow-up singularities. 
Rugang Ye