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Half-plane capacity and conformal radius


Authors: Steffen Rohde and Carto Wong
Journal: Proc. Amer. Math. Soc. 142 (2014), 931-938
MSC (2010): Primary 30C99
DOI: https://doi.org/10.1090/S0002-9939-2013-11811-3
Published electronically: December 4, 2013
MathSciNet review: 3148527
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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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Additional Information

Steffen Rohde
Affiliation: Department of Mathematics, C-337 Padelford Hall, Box 354350, University of Washington, Seattle, Washington 98195-4350
Email: rohde@math.washington.edu

Carto Wong
Affiliation: Department of Mathematics, C-337 Padelford Hall, Box 354350, University of Washington, Seattle, Washington 98195-4350
Email: carto@u.washington.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11811-3
Keywords: Complex analysis, geometric function theory, half-plane capacity, conformal radius
Received by editor(s): February 9, 2012
Received by editor(s) in revised form: April 10, 2012
Published electronically: December 4, 2013
Additional Notes: The first author’s research was supported in part by NSF Grant DMS-0800968.
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.