TY - JOUR
T1 - Capacity, quasi-local mass, and singular fill-ins
AU - Mantoulidis, Christos
AU - Miao, Pengzi
AU - Tam, Luen Fai
N1 - Publisher Copyright:
© 2020 Walter de Gruyter GmbH, Berlin/Boston.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/11/1
Y1 - 2020/11/1
N2 - 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.
AB - 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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U2 - 10.1515/crelle-2019-0040
DO - 10.1515/crelle-2019-0040
M3 - Article
AN - SCOPUS:85077742271
VL - 2020
SP - 55
EP - 92
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 768
ER -