2012/01/27 by Steffen Rohde, Rohde, Steffen, Carto Wong +1
Mathematics · #Algebraic and Geometric Analysis #Analytic and geometric function theory #Holomorphic and Operator Theory #math.CV
paper · pdf · doi:10.48550/arxiv.1201.5878
9 pages, 4 figures
arxiv created 2012/01/27 · arxiv updated 2012/01/30
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.