{"paper":{"title":"Critical points of Wang-Yau quasi-local energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Luen-fai Tam, Naqing Xie, Pengzi Miao","submitted_at":"2010-03-26T06:42:56Z","abstract_excerpt":"In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced metric on $\\Sigma$ has positive Gaussian curvature and all boundary components of $\\Omega$ have positive mean curvature. Suppose $H \\le H_0$ where $H$ is the mean curvature of $\\Sigma$ in $\\Omega$ and $H_0$ is the mean curvature of $\\Sigma$ when isometrically embedded in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5048","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}