The gradient flow of the L² curvature energy near the round sphere

2010/03/08 by Jeff Streets, Streets, Jeff · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1003.1707

openalex publication_date 2010/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the low-energy behavior of the gradient flow of the L² norm of the Riemannian curvature on four-manifolds. Specifically, we show long time existence and exponential convergence to a metric of constant sectional curvature when the initial metric has positive Yamabe constant and small initial energy.

Cited by

• The long time behavior of fourth-order curvature flows
• Collapsing in the L² curvature flow

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