Communications in Analysis and Geometry

Volume 19 (2011)

Number 5

Curvature pinching estimate and singularities of the Ricci flow

Pages: 975 – 990



Xiaodong Cao (Department of Mathematics, Cornell University)


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.

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