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arXiv · 1805.05493

Capacity, quasi-local mass, and singular fill-ins

Christos Mantoulidis·Pengzi Miao·Luen-Fai Tam
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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.

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Christos Mantoulidis, Pengzi Miao, Luen-Fai Tam. 2018-05-14. Capacity, quasi-local mass, and singular fill-ins. https://doi.org/10.1515/crelle-2019-0040

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