Half-plane capacity and conformal radius

Steffen Rohde; Carto Wong

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arXiv · 1201.5878

Half-plane capacity and conformal radius

Steffen Rohde·Carto Wong

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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.

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Steffen Rohde, Carto Wong. 2012-01-27. Half-plane capacity and conformal radius. https://arxiv.org/abs/1201.5878

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