发表机构
Human-Centered Artificial Intelligence Research Institute, Ewha Womans University（韩国女子大学人类中心人工智能研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明在非负数量曲率且渐近平坦的完备流形上，ADM 质量受向外极小化 $p$-容量下确界控制，等号刻画 Schwarzschild 外部并揭示视界，容量间隙可检测视界。
AI 中文摘要
设 $(M^3,g)$ 为微分同胚于 $\R^3\setminus\{0\}$ 的完备黎曼流形，其数量曲率非负。假设一个指定的端渐近平坦，ADM 质量为 $m_+$。对每个 $p\in(1,3)$，定义 $c_{O,p}$ 为在分离两个端的向外极小化有限周长边界上，Schwarzschild 归一化 $p$-容量的下确界。我们证明当 $A(g)>0$ 时 $m_+\ge c_{O,p}$，其中 $A(g)$ 为分离两个端的边界面积的下确界。在单个指数处取等号产生一个最小面积视界，迫使其外部为质量 $m_+$ 的 Schwarzschild 外部，并在所有指数处取等号。在取等号情形下，若第二个端也渐近平坦，则其质量满足 $m_-\ge m_+$，且等号恰对应双侧空间 Schwarzschild 流形。我们还证明 $c_{O,p}$ 与无约束容量下确界 $c_{M,p}$ 之间的严格间隙可检测视界的存在。
英文摘要
Let $(M^3,g)$ be a complete Riemannian manifold diffeomorphic to $\R^3\setminus\{0\}$, with nonnegative scalar curvature. Assume that a distinguished end is asymptotically flat, with ADM mass $m_+$. For each $p\in(1,3)$, define $c_{O,p}$ as the infimum of the Schwarzschild-normalized $p$-capacity over outward-minimizing finite-perimeter boundaries separating the two ends. We prove that $m_+\ge c_{O,p}$ whenever $A(g)>0$, where $A(g)$ is the infimum of the areas of boundaries separating the two ends. Equality at a single exponent produces a least-area horizon, forces its exterior to be the Schwarzschild exterior of mass $m_+$, and yields equality at every exponent. In the equality case, if the second end is also asymptotically flat, its mass satisfies $m_-\ge m_+$, with equality precisely for the two-sided spatial Schwarzschild manifold. We also show that a strict gap between $c_{O,p}$ and the unconstrained capacity infimum $c_{M,p}$ detects a horizon.
