Half-plane capacity and conformal radius
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- by Steffen Rohde and Carto Wong PDF
- Proc. Amer. Math. Soc. 142 (2014), 931-938 Request permission
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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 931-938
- MSC (2010): Primary 30C99
- DOI: https://doi.org/10.1090/S0002-9939-2013-11811-3
- MathSciNet review: 3148527