Mathematical Research Letters

Volume 20 (2013)

Number 5

Local pinching estimates in 3-dim Ricci flow

Pages: 845 – 855



Bing-Long Chen (Department of Mathematics, Sun Yat-Sen University, Guangzhou, China)

Guoyi Xu (Mathematical Sciences Center, Tsinghua University, Beijing, China)

Zhuhong Zhang (Department of Mathematics, South China Normal University, Guangzhou, China)


We study curvature pinching estimates of Ricci flow on complete three-dimensional (3-dim) manifolds without bounded curvature assumption. We will derive some general curvature conditions which are preserved on any complete solution of 3-dim Ricci flow, these conditions include nonnegative Ricci curvature and sectional curvature as special cases. A local version of Hamilton-Ivey estimates is also obtained.


Ricci flow, local estimate

2010 Mathematics Subject Classification

35K40, 53C44

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