发表机构
Beijing Institute of Mathematical Sciences and Applications（北京国际数学研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将黎曼正质量定理的Dong-Song稳定性定理推广到高维自旋流形，通过构造全局极小图的坐标并利用旋子控制度量缺陷，证明对应外部区域在特定拓扑下收敛于欧氏空间。
AI 中文摘要
我们将黎曼正质量定理的Dong-Song稳定性定理推广到更高维的自旋流形。更确切地说，对于一列具有非负标量曲率且ADM质量趋于零的完备渐近平坦自旋n流形，通过切除边界面积趋于零的区域得到的外部区域，在有向测量Gromov-Hausdorff拓扑中收敛于欧氏空间。该证明从全局极小图构造坐标，并利用旋子控制度量缺陷。
英文摘要
We prove stability of the Riemannian positive mass theorem in all dimensions, extending the Dong-Song stability theorem. For a sequence of complete asymptotically flat manifolds with nonnegative scalar curvature and ADM masses tending to zero, excising domains whose boundary areas tend to zero yields exterior regions converging to Euclidean space in the pointed measured Gromov-Hausdorff topology. The proof constructs global coordinates from minimal graphs and controls their Hessians using scalar solutions of the conformal Laplace equation on the associated graph metrics.
CommentsRevised version. The spin assumption has been removed
