Duke Mathematical Journal

A general convergence result for the Ricci flow in higher dimensions

Simon Brendle

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Abstract

Let $(M, g_{0})$ be a compact Riemannian manifold of dimension $n{\geq}4$. We show that the normalized Ricci flow deforms $g_{0}$ to a constant curvature metric, provided that $(M, g_{0})\times\mathbb{R}$ has positive isotropic curvature. This condition is stronger than two-positive flag curvature but weaker than two-positive curvature operator

Article information

Source
Duke Math. J. Volume 145, Number 3 (2008), 585-601.

Dates
First available in Project Euclid: 15 December 2008

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1229349905

Digital Object Identifier
doi:10.1215/00127094-2008-059

Mathematical Reviews number (MathSciNet)
MR2462114

Zentralblatt MATH identifier
1161.53052

Subjects
Primary: 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Citation

Brendle, Simon. A general convergence result for the Ricci flow in higher dimensions. Duke Math. J. 145 (2008), no. 3, 585--601. doi:10.1215/00127094-2008-059. http://projecteuclid.org/euclid.dmj/1229349905.


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References

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