On geometric problems related to Brown-York and Liu-Yau quasilocal mass

DOI10.1007/s00220-010-1042-7zbMath1200.58018arXiv0906.5451OpenAlexW2167424953MaRDI QIDQ1958534

Pengzi Miao, Yuguang Shi, Luen-Fai Tam

Publication date: 4 October 2010

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.5451

zbMATH Keywords

quasilocal massBrown-York massLiu-Yau mass

Mathematics Subject Classification ID

Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Applications of differential geometry to physics (53Z05) General relativity (83C99) Applications of variational problems in infinite-dimensional spaces to the sciences (58E50)

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Total mean curvature of the boundary and nonnegative scalar curvature fill-ins ⋮ Mathematical general relativity: A sampler ⋮ Quasi-local mass via isometric embeddings: a review from a geometric perspective ⋮ Some functionals on compact manifolds with boundary ⋮ Deformation of scalar curvature and volume ⋮ The Dirac operator on untrapped surfaces ⋮ Extension of a theorem of Shi and Tam ⋮ The initial boundary value problem and quasi-local Hamiltonians in general relativity ⋮ Total mean curvature, scalar curvature, and a variational analog of Brown-York mass ⋮ Quasi-local energy-momentum and angular momentum in general relativity ⋮ Critical points of Wang-Yau quasi-local energy ⋮ Three-dimensional Ricci-degenerate Riemannian manifolds satisfying geometric equations ⋮ A holographic principle for the existence of imaginary Killing spinors

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