Convergence of the Ricci flow on asymptotically flat manifolds with integral curvature pinching

DOI10.2422/2036-2145.202001_007zbMath1494.53103arXiv1907.13189OpenAlexW3141679228MaRDI QIDQ5075122

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Publication date: 10 May 2022

Published in: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.13189

zbMATH Keywords

curvature pinchinglong-time existencescale-invariant integral norm

Mathematics Subject Classification ID

Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Ricci flows (53E20)

Related Items (2)

Ricci flow and a sphere theorem for \(L^{n/2}\)-pinched Yamabe metrics ⋮ Small curvature concentration and Ricci flow smoothing

Cites Work

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• Extremal of log Sobolev inequality and \(W\) entropy on noncompact manifolds
• Stability of Euclidean space under Ricci flow
• Ricci deformation of the metric on a Riemannian manifold
• Deforming the metric on complete Riemannian manifolds
• Effective \(L_p\) pinching for the concircular curvature
• Ricci deformation of the metric on complete non-compact Riemannian manifolds
• Ricci flow on asymptotically Euclidean manifolds
• Bach-flat asymptotically locally Euclidean metrics
• Three-manifolds with positive Ricci curvature
• Integral pinching theorems
• An exact sequence in \(L^2\)-cohomology
• The logarithmic Sobolev and Sobolev inequalities along the Ricci flow
• Manifolds with positive curvature operators are space forms
• Uniqueness of the Ricci flow on complete noncompact manifolds
• Mass under the Ricci flow
• Einstein manifolds
• Rotationally symmetric Ricci flow on asymptotically flat manifolds
• Manifolds with 1/4-pinched curvature are space forms
• Ricci Flow, Einstein Metrics and Space Forms
• L p pinching and compactness theorems for compact Riemannian manifolds
• The ricci flow on radially symmetric R³
• Optimal Sobolev Inequalities on Complete Riemannian Manifolds with Ricci Curvature Bounded Below and Positive Injectivity Radius
• Local derivative estimates for the heat equation coupled to the Ricci flow
• A Uniform Sobolev Inequality Under Ricci Flow
• A harnack inequality for parabolic differential equations
• The Gauss-Bonnet Theorem for Riemannian Polyhedra

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