奇异环面静态模型的正质量型定理
A Positive Mass Type Theorem for a Singular Toroidal Static Model
- Shanghai Jiao Tong University（上海交通大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文利用逆平均曲率流和Shi-Tam型构造，为具有平坦环面切片的静态空间模型的三维流形建立了正质量型定理及Brown-York型不等式，并探讨了推广障碍及负质量与内部奇异性和拓扑的关系。
AI中文摘要：
我们研究以具有平坦环面切片的静态空间为模型的三维流形上的正质量及相关Brown-York型不等式。利用逆平均曲率流，我们首先推导出一个不等式，将无穷远处的渐近几何与内部奇异性的大小联系起来。该不等式可自然地解释为正质量型定理。然后，我们将此全局不等式与Shi-Tam型构造相结合，得到对于等距于平坦环面的边界成立的一个Brown-York型不等式。与Schwarzschild情形相比，我们的论证不能直接推广到一般边界曲面，并且我们指出了若干阻碍这种推广的障碍。最后，我们讨论了一些例子，用以说明负质量、内部奇异性的强度以及内部拓扑之间的关系。
英文摘要：
We study positive mass and related Brown--York type inequalities for three-dimensional manifolds modeled on a static space with flat toroidal slices. Using inverse mean curvature flow, we first derive an inequality relating the asymptotic geometry at infinity to the size of an interior singularity. This inequality admits a natural interpretation as a positive mass type theorem. We then combine this global inequality with a Shi--Tam type construction to obtain a Brown--York type inequality for boundaries isometric to flat tori. In contrast to the Schwarzschild setting, our argument does not extend directly to general boundary surfaces, and we identify several obstructions to such a generalization. Finally, we discuss examples illustrating the relationship between negative mass, the strength of interior singularities, and the topology of the interior.
