Communications in Analysis and Geometry

Volume 19 (2011)

Number 5

Curvature pinching estimate and singularities of the Ricci flow

Pages: 975 – 990

DOI: http://dx.doi.org/10.4310/CAG.2011.v19.n5.a6

Author

Xiaodong Cao (Department of Mathematics, Cornell University)

Abstract

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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