## Duke Mathematical Journal

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

### A general convergence result for the Ricci flow in higher dimensions

#### 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.