A complete proof of Hamilton's conjecture

2010/08/09 by Li Ma, Ma, Li · 2 citations
Mathematics · Physics and Astronomy · #53CXX #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1008.1576

openalex publication_date 2010/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give the full proof of a conjecture of R.Hamilton that for (M³, g) being a complete Riemannian 3-manifold with bounded curvature and with the Ricci pinching condition Rc≥ \ep R g, where R>0 is the positive scalar curvature and \ep>0 is a uniform constant, M³ is compact. One of the key ingredients to exclude the local collapse in singularities of the Ricci flow is the use of pinching-decaying estimate. The other important part of our argument is to role out the Type III singularity complete noncompact Ricci flow with positive Ricci pinching condition. We get this goal by obtaining an Ricci expander based on the monotonicity formula of weighted reduced volume.

Citations

• A Compactness Property for Solutions of the Ricci Flow

Cited by

• Injectivity radius bound of Ricci flow with positive Ricci curvature and applications
• On the weighted forward reduced Entropy of Ricci flow

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