Capacity, quasi-local mass, and singular fill-ins
Capacity, quasi-local mass, and singular fill-ins
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DOI：
10.1515/crelle-2019-0040
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Christos Mantoulidis;P. Miao;Luen-Fai Tam
中科院分区：
文献类型：
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作者：
Christos Mantoulidis;P. Miao;Luen-Fai Tam
摘要我们导出了具有非负标量曲率的渐近平坦三维流形的边界容量与与准局部质量有关的边界量之间的新的不等式；一个与Brown-York质量有关，另一个是新的。我们重塑了具有非负数量曲率的均值-凸填充的研究框架，在此过程中，我们考虑了可能具有独立兴趣的具有奇异度量的填充。其中，我们的工作得到了黎曼Schwarzschild流形的新的变分刻画和其中的曲面的新的比较结果。
Abstract We derive new inequalities between the boundary capacity of an asymptotically flat 3-manifold with nonnegative scalar curvature and boundary quantities that relate to quasi-local mass; one relates to Brown–York mass and the other is new. We argue by recasting the setup to the study of mean-convex fill-ins with nonnegative scalar curvature and, in the process, we consider fill-ins with singular metrics, which may have independent interest. Among other things, our work yields new variational characterizations of Riemannian Schwarzschild manifolds and new comparison results for surfaces in them.