Curvature pinching estimate and singularities of the Ricci flow

摘要

In this paper, we first derive a pinching estimate on the traceless Ricci curvature in term of scalar curvature and Weyl tensor under the Ricci flow. This generalizes a previous result of Knopf [15]. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Wevl tensor has to blow up at least at a certain rate.