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.

中文翻译：

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容量，准局部质量和奇异填充

我们推导了具有非负标量曲率的渐近平坦3形流形的边界容量和与拟局部质量有关的边界量之间的新不等式。一个与布朗-约克质量有关，另一个与之有关。我们通过将设置重铸为具有非负标量曲率的均值凸填充的研究来进行争论，并且在此过程中，我们考虑具有奇异度量的填充，这些度量可能具有独立的兴趣。除其他事项外，我们的工作产生了黎曼Schwarzschild流形的新的变分特征，以及其中的曲面的新比较结果。