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

DOI10.1016/j.aim.2021.108054zbMath1482.53122OpenAlexW3207082333MaRDI QIDQ2054239

Yanyan Li

Publication date: 1 December 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2021.108054

zbMATH Keywords

Ricci flowcurvature pinchingintegral curvaturesphere theoremYamabe metrics

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Conformal structures on manifolds (53C18) Ricci flows (53E20)

Related Items (1)

Some aspects of Ricci flow on the 4-sphere

Cites Work

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• The gradient flow of the \(L^2\) curvature energy near the round sphere
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Ricci deformation of the metric on a Riemannian manifold
• A sharp characterization of the smooth 4-sphere in curvature terms
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• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• A sphere theorem for three dimensional manifolds with integral pinched curvature
• A conformally invariant sphere theorem in four dimensions
• The logarithmic Sobolev and Sobolev inequalities along the Ricci flow
• Ricci Flow, Einstein Metrics and Space Forms
• L p pinching and compactness theorems for compact Riemannian manifolds
• Convergence of the Ricci flow on asymptotically flat manifolds with integral curvature pinching

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