Removable singularity of positive mass theorem with continuous metrics

2020/12/28 by Wenshuai Jiang, Weimin Sheng, Jiang, Wenshuai +3 · 1 citation
Mathematics · #53C20 #83C99 #Bounded function #Combinatorics #Conjecture #Curvature #Differential Geometry (math.DG) #Euclidean space #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Partial Differential Equations #Physics #Quantum mechanics #Ricci curvature #Scalar curvature #Sigma #math.DG #msc:53C20 #msc:83C99

paper · pdf · doi:10.48550/arxiv.2012.14041

35 pages

arxiv created 2020/12/28 · openalex publication_date 2020/12/28 · arxiv updated 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In this paper, we consider asymptotically flat Riemannnian manifolds (Mⁿ,g) with C⁰ metric g and g is smooth away from a closed bounded subset Σ and the scalar curvature R_g≥ 0 on M∖ Σ. For given n≤ p≤ ∞, if g∈ C⁰∩ W^1,p and the Hausdorff measure H^n-(p)/(p-1)(Σ)

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• Positive mass theorems for singular asymptotically hyperbolic manifolds

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