Extensions and fill-ins with non-negative scalar curvature
Extensions and fill-ins with non-negative scalar curvature
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DOI：
10.1088/0264-9381/30/19/195007
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发表时间：
2013-04
影响因子：
3.5
通讯作者：
Jeffrey L. Jauregui;P. Miao;Luen-Fai Tam
中科院分区：
文献类型：
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作者：
Jeffrey L. Jauregui;P. Miao;Luen-Fai Tam
受广义相对论中准局域质量问题的启发，我们应用Shi和Tam在证明Brown-York质量正性时构造的渐近平坦扩展，来研究在2-球体上实现几何数据作为非负标量曲率的紧致3-流形边界的填充问题。我们描述了两种边界情况之间的关系：一种是 Shi-Tam 延伸的总质量为零，另一种是非负标量曲率的填充不存在。此外，我们在后一种情况下证明了一种正质量定理。
Motivated by the quasi-local mass problem in general relativity, we apply the asymptotically flat extensions, constructed by Shi and Tam in the proof of the positivity of the Brown–York mass, to study a fill-in problem of realizing geometric data on a 2-sphere as the boundary of a compact 3-manifold of non-negative scalar curvature. We characterize the relationship between two borderline cases: one in which the Shi–Tam extension has zero total mass, and another in which fill-ins of non-negative scalar curvature fail to exist. Additionally, we prove a type of positive mass theorem in the latter case.