  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.

Differential Geometry