Half-plane capacity and conformal radius
Complex Variables
2012-01-30 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1201.5878,
title = {Half-plane capacity and conformal radius},
author = {Steffen Rohde and Carto Wong},
journal= {arXiv preprint arXiv:1201.5878},
year = {2012}
}
Comments
9 pages, 4 figures