Convergence of the Yamabe flow in dimension 6 and higher

2007/08/24 by Simon Brendle · 146 citations
Mathematics · #Convergence (economics) #Curvature #Dimension (graph theory) #Flow (mathematics) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Pure mathematics #Scalar curvature #Sectional curvature #Yamabe flow

paper · doi:10.1007/s00222-007-0074-x

published in Inventiones mathematicae 170(3), 541-576 (Springer Science+Business Media)

openalex publication_date 2007/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Citations

• The yamabe flow on locally conformally flat manifolds with positive ricci curvature
• On the proof of the positive mass conjecture in general relativity
• The mass of an asymptotically flat manifold
• A new proof of the positive energy theorem

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• Ricci flow on surfaces along the standard lightcone in the 3+1-Minkowski spacetime
• Recent progress on the Yamabe problem
• Asymptotic large time behavior of singular solutions of the fast diffusion equation
• Extending Yamabe flow on complete Riemannian manifolds
• Complete quasi-Yamabe gradient solitons with bounded scalar curvature
• A compactness result for scalar-flat metrics on manifolds with umbilic boundary
• A positive mass theorem in three dimensional Cauchy–Riemann geometry
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• Simon Brendle [wikipedia]