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Curvature Pinching Estimate And Singularities Of The Ricci Flow

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. Then we apply this estimate to study finite-time singularity behavior. We show that if the scalar curvature is uniformly bounded, then the Weyl tensor has to blow up, as a consequence, the corresponding singularity model must be Ricci flat with non-vanishing Weyl tensor.

preprint2010arXivOpen access
Xiaodong Cao
math.DG
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Xiaodong Cao

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