Half-plane capacity and conformal radius

Details Half-plane capacity and conformal radius Half-plane capacity and conformal radius

2012-01-27

arxiv.org/abs/1201.5878v1

Mathematics

Complex Variables

9 pages, 4 figures

Scientific paper

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.

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