Curvature pinching estimate and singularities of the Ricci flow

In this paper, we first derive a pinching estimate on thetraceless Ricci curvature in term of scalar curvature andWeyl tensor under the Ricci flow. This generalizes aprevious result of Knopf. Then we applythis estimate to study finite-time singularity behavior. Weshow that if the scalar curvature is uniformly bounded,then the Weyl tensor has to blow up at least at a certainrate.

Full Text (PDF format)

Published 3 February 2012