Half-plane capacity and conformal radius
Half-plane capacity and conformal radius
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DOI：
10.1090/s0002-9939-2013-11811-3
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发表时间：
2012-01
期刊：
影响因子：
--
通讯作者：
S. Rohde;Carto Wong
中科院分区：
文献类型：
--
作者：
S. Rohde;Carto Wong
本文证明了上半平面的一个子集的半平面容量相当于一个简单的几何量，即该集合中半径为1的双曲邻域的欧氏面积.这是通过证明一个类似的估计单位圆盘的子域的共形半径，并通过建立这两个量之间的简单关系。
In this note, we show that the half-plane capacity of a subset of the upper half-plane is comparable to a simple geometric quantity, namely the euclidean area of the hyperbolic neighborhood of radius one of this set. This is achieved by proving a similar estimate for the conformal radius of a subdomain of the unit disc, and by establishing a simple relation between these two quantities.