论文标题
冷凝器容量和双曲直径
Condenser capacity and hyperbolic diameter
论文作者
论文摘要
鉴于单位磁盘$ \ mathbb {b}^{2} $中的紧凑型连接集合$ e $，我们为冷凝器$（\ Mathbb {b}^{2}，e）提供了一个新的上限，以增强$ t $ o的$ e $ $ e $ $ t $ t $ t $ t $ t $ t $ t $。此外，对于$ t> 0 $，我们构建了一组双曲直径$ t $，并应用新颖的数值方法表明它的容量要比直径相同的双曲线磁盘更大。我们构造的集合称为双曲线几何形状中的Reuleaux三角形，它的双曲线宽度等于$ t $。
Given a compact connected set $E$ in the unit disk $\mathbb{B}^{2}$, we give a new upper bound for the conformal capacity of the condenser $(\mathbb{B}^{2}, E)$ in terms of the hyperbolic diameter $t$ of $E$. Moreover, for $t>0$, we construct a set of hyperbolic diameter $t$ and apply novel numerical methods to show that it has larger capacity than a hyperbolic disk with the same diameter. The set we construct is called a Reuleaux triangle in hyperbolic geometry and it has constant hyperbolic width equal to $t$.
