球ECD时空的CMC曲面和面积电荷不等式
CMC surfaces and area-charge inequality for a spheroidal ECD spacetime
摘要：
我们考虑Bonnor \cite{Bonnor98}提出的时空，它的物质内容是一个电平衡的尘埃球体，在面积和电荷之间的几何不等式的背景下。我们确定数值的常平均曲率的表面是稳定的等周面的候选人，并分析它们的面积和电荷之间的关系，表明以前证明的不等式是远远没有饱和。我们还表明，最大的初始数据有一个圆柱形的限制，最小的面积电荷关系达到。
英文摘要：
We consider the spacetime presented by Bonnor \cite{Bonnor98}, whose matter content is a spheroid of electrically counterpoised dust, in the context of the geometrical inequalities between area and charge. We determine numerically the constant mean curvature surfaces that are candidates to be stable isoperimetric surfaces and analyze the relation between area and charge for them, showing that a previously proved inequality is far from being saturated. We also show that the maximal initial data has a cylindrical limit where the minimum of the area-charge relation is attained.
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