On the conditions to extend Ricci flow(II)

Abstract

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: $\underset{X}{\sup }|Ric|$ and $\sqrt{\underset{X}{\sup }|Rm|}\cdot \sqrt{\underset{X}{\sup }|R|}$ must blowup at least at the rate of type-I. Our estimates also imply some gap theorems for shrinking Ricci solitons.

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

References in corpus (6)

• Ricci Flow and the Poincare Conjecture
• Perelman's reduced volume and a gap theorem for the Ricci flow
• Remarks on curvature behavior at the first singular time of the Ricci flow
• Remarks on non-compact gradient Ricci solitons
• Curvature Pinching Estimate And Singularities Of The Ricci Flow
• The Curvature of Gradient Ricci Solitons