English

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

R2 v1 2026-06-21T20:10:53.463Z