Capacity, quasi-local mass, and singular fill-ins-Reference-Cited by-同舟云学术

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

Published:2019-12-19 Issue:768 Volume:2020 Page:55-92
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Mantoulidis Christos¹^ORCID,Miao Pengzi²^ORCID,Tam Luen-Fai³^ORCID

Affiliation:

1. Department of Mathematics , Massachusetts Institute of Technology , Cambridge , MA 02139 , USA

2. Department of Mathematics , University of Miami , Coral Gables , FL 33146 , USA

3. The Institute of Mathematical Sciences and Department of Mathematics , The Chinese University of Hong Kong , Shatin , Hong Kong , P. R. China

Abstract

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.

Funder

National Science Foundation

Royal Swedish Academy of Sciences

Research Grants Council, University Grants Committee

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2019-0040/pdf

Reference36 articles.

1. V. Agostiniani and L. Mazzieri, On the geometry of the level sets of bounded static potentials, Comm. Math. Phys. 355 (2017), no. 1, 261–301.

2. V. Agostiniani and L. Mazzieri, Monotonicity formulas in potential theory, Calc. Var. Partial Differential Equations 59 (2020), no. 1, Paper No. 6.

3. R. Arnowitt, S. Deser and C. W. Misner, Dynamical structure and definition of energy in general relativity, Phys. Rev. (2) 116 (1959), 1322–1330.

4. H. Bray and P. Miao, On the capacity of surfaces in manifolds with nonnegative scalar curvature, Invent. Math. 172 (2008), no. 3, 459–475.

5. H. Bray and F. Morgan, An isoperimetric comparison theorem for Schwarzschild space and other manifolds, Proc. Amer. Math. Soc. 130 (2002), no. 5, 1467–1472.

Cited by 12 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Mass, Capacitary Functions, and the Mass-to-Capacity Ratio;Peking Mathematical Journal;2023-06-08

2. On a class of regions with maximal total mean curvature boundary;SCIENTIA SINICA Mathematica;2023-05-01

3. Metrics with $$\lambda _1(-\Delta + k R) \ge 0$$ and Flexibility in the Riemannian Penrose Inequality;Communications in Mathematical Physics;2023-03-04

4. The asymptotic behaviour of p-capacitary potentials in asymptotically conical manifolds;Mathematische Annalen;2022-11-27

5. First Boundary Dirac Eigenvalue and Boundary Capacity Potential;Annales Henri Poincaré;2022-09-16