On the conditions to extend Ricci flow(II)

Details On the conditions to extend Ricci flow(II) On the conditions to extend Ricci flow(II)

2011-07-26

arxiv.org/abs/1107.5107v1

Mathematics

Differential Geometry

27 pages, 3 figures; Int Math Res Notices (2011)

Scientific paper

10.1093/imrn/rnr141

We develop some estimates under the Ricci flow and use these estimates to study the blowup rates of curvatures at singularities. As applications, we obtain some gap theorems: $\displaystyle \sup_X |Ric|$ and $\displaystyle \sqrt{\sup_X |Rm|} \cdot \sqrt{\sup_X |R|}$ must blowup at least at the rate of type-I. Our estimates also imply some gap theorems for shrinking Ricci solitons.

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