Heat kernel and curvature bounds in Ricci flows with bounded scalar curvature

Using the backward pseudolocality theorem, we next establish a uniform L2 curvature bound in dimension 4 and we show that the flow in dimension 4 converges to an orbifold at a singularity. We also obtain a stronger ε-regularity theorem for Ricci flows. This result is particularly useful in the study of Kähler Ricci flows on Fano manifolds, where it can be used to derive certain convergence results.