A general convergence result for the Ricci flow in higher dimensions

2008/12/01 by Simon Brendle · 1 citation
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Advanced Differential Geometry Research #Ricci flow #Mathematics #Convergence (economics) #Flow (mathematics) #Pure mathematics #Ricci curvature #Geometry #Economics

paper · doi:10.1215/00127094-2008-059

openalex publication_date 2008/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/14

Abstract

Let (M,g0) be a compact Riemannian manifold of dimension n≥4. We show that the normalized Ricci flow deforms g0 to a constant curvature metric, provided that (M,g0)×R has positive isotropic curvature. This condition is stronger than two-positive flag curvature but weaker than two-positive curvature operator

Citations

• Four-manifolds with positive isotropic curvature
• Three-manifolds with positive Ricci curvature
• Manifolds with 1/4-pinched curvature are space forms

Cited by

• Ricci flow [wikipedia]

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