论文标题
ADM质量和无穷大的容量 - 体积赤字
ADM mass and the capacity-volume deficit at infinity
论文作者
论文摘要
G. Huisken基于等术不平等，提出了总体相对论的总质量的定义，其等效于ADM质量（平滑）非负标量曲率的3型含量（平滑），但在更大的一般性方面是明确定义的。同样，我们使用异阵态不平等（在数量方面的边界能力）来提出对总质量的新定义。我们证明了IT与ADM质量之间的不平等，并证明了与谐波渐近的渐近不平等，或者与一般渐近学有关球的疲劳（而不是任意紧凑的集合）。这种质量方法可能会应用于涉及一般相对论中涉及低规律性指标和收敛性低的问题，并且相对于等级质量质量可能具有一定的优势。提出了一些猜想，即CMC表面的已知结果类似物和等值区。
Based on the isoperimetric inequality, G. Huisken proposed a definition of total mass in general relativity that is equivalent to the ADM mass for (smooth) asymptotically flat 3-manifolds of nonnegative scalar curvature, but that is well-defined in greater generality. In a similar vein, we use the isocapacitary inequality (bounding capacity from below in terms of volume) to suggest a new definition of total mass. We prove an inequality between it and the ADM mass, and prove the reverse inequality with harmonically flat asymptotics, or, with general asymptotics, for exhaustions by balls (as opposed to arbitrary compact sets). This approach to mass may have applications to problems involving low regularity metrics and convergence in general relativity, and may have some advantages relative to the isoperimetric mass. Some conjectures, analogs of known results for CMC surfaces and isoperimetric regions, are proposed.
