The gradient flow of the \(L^2\) curvature energy near the round sphere

DOI10.1016/j.aim.2012.05.011zbMath1252.53081arXiv1003.1707OpenAlexW2964123288MaRDI QIDQ436175

Jeffrey Streets

Publication date: 30 July 2012

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

Full work available at URL: https://arxiv.org/abs/1003.1707

zbMATH Keywords

exponential convergencelong time existencefour manifoldmetric of constant sectional curvaturepositive Yamabe constantRiemannian curvature gradient flowsmall energy

Mathematics Subject Classification ID

Related Items (6)

The geometric triharmonic heat flow of immersed surfaces near spheres ⋮ The long time behavior of fourth order curvature flows ⋮ Conformal bach flow ⋮ Convergence of Riemannian 4-manifolds with \(L^2\)-curvature bounds ⋮ Ricci flow and a sphere theorem for \(L^{n/2}\)-pinched Yamabe metrics ⋮ Collapsing in theL²Curvature Flow

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The gradient flow of the \(L^2\) curvature functional with small initial energy
• The gradient flow of \(\int _M|Rm|^{2}\)
• Conformal deformation of a Riemannian metric to constant scalar curvature
• Four-manifolds with positive curvature operator
• Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire
• Four-manifolds with \(\delta W^+=0\) and Einstein constants of the sphere.
• The Willmore flow with small initial energy.
• Removability of point singularities of Willmore surfaces
• Bach-flat asymptotically locally Euclidean metrics
• Curvature and critical Riemannian metric
• A conformally invariant sphere theorem in four dimensions
• Moduli spaces of critical Riemannian metrics in dimension four
• On conformally Kähler, Einstein manifolds
• Ricci Flow, Einstein Metrics and Space Forms
• Convergence of riemannian manifolds with integral bounds on curvature. I
• Convergence of riemannian manifolds with integral bounds on curvature. II
• Quelques formules de variation pour une structure riemannienne

This page was built for publication: The gradient flow of the \(L^2\) curvature energy near the round sphere