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

2019/07/30 by Chen, Eric · 1 citation
#53C44 (Primary) #58J35 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1907.13189

Abstract

We prove a curvature pinching result for the Ricci flow on asymptotically flat manifolds: if an asymptotically flat manifold of dimension n≥ 3 has scale-invariant integral norm of curvature sufficiently pinched relative to the inverse of its Sobolev constant, then the Ricci flow starting from this manifold exists for all positive times and converges to flat Euclidean space. In particular our result implies that the initial manifold must have been diffeomorphic to ℝⁿ.

Cited by

• Local mollification of metrics with small curvature concentration

Related

• Long-time Ricci flow existence and topological rigidity from manifolds with pinched scale-invariant integral curvature
• Initial stability estimates for Ricci flow and three dimensional Ricci-pinched manifolds
• Three-manifolds with non-negatively pinched Ricci curvature
• A pinching estimate for solutions of the linearized Ricci flow system on 3-manifolds
• Curvature Estimates for the Ricci Flow II