论文标题
冷凝器容量的等级特性
Isoperimetric properties of condenser capacity
论文作者
论文摘要
对于单位磁盘$ \ mathbb {d} $的紧凑型子集$ e $，我们通过按双曲几何形状定义的集合功能来研究冷凝器$ {\ rm cap}（\ mathbb {d}，e）$的容量。特别是，我们通过实验研究双曲线三角形的情况，并得出了所有具有相同双曲区域的三角形的猜想，等边三角形的容量最小。
For compact subsets $E$ of the unit disk $ \mathbb{D}$ we study the capacity of the condenser ${\rm cap}( \mathbb{D},E)$ by means of set functionals defined in terms of hyperbolic geometry. In particular, we study experimentally the case of a hyperbolic triangle and arrive at the conjecture that of all triangles with the same hyperbolic area, the equilateral triangle has the least capacity.
