Asymptotic Curvature Decay and Removal of Singularities of Bach-Flat Metrics

2007/08/07 by Jeffrey Streets, Streets, Jeffrey · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AP #math.DG

paper · pdf · doi:10.48550/arxiv.0708.0869

arxiv created 2007/08/07 · openalex publication_date 2007/08/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a removal of singularities result for Bach-flat metrics in dimension 4 under the assumption of bounded L² norm of curvature, bounded Sobolev constant and a volume growth bound. This result extends the removal of singularities result for special classes of Bach-flat metrics obtained in \citeTVMOD. For the proof we analyze the decay rates of solutions to the Bach-flat equation linearized around a flat metric. This classification is used to prove that Bach-flat cones are in fact ALE of order τ for any τ< 2. This result is then used to prove the removal of singularities theorem.

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• Weyl energy and connected sums of four-manifolds

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