Lengths of radii under conformal maps of the unit disc
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- by Zoltan Balogh and Mario Bonk PDF
- Proc. Amer. Math. Soc. 127 (1999), 801-804 Request permission
Abstract:
If $E_{f}(R)$ is the set of endpoints of radii which have length greater than or equal to $R>0$ under a conformal map $f$ of the unit disc, then $\operatorname {cap} E_{f}(R)=O(R^{-1/2})$ as $R\to \infty$ for the logarithmic capacity of $E_{f}(R)$. The exponent $-1/2$ is sharp.References
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Additional Information
- Zoltan Balogh
- Affiliation: Universität Bern, Mathematisches Institut, Sidlerstr. 5, CH-3012 Bern, Switzerland
- Email: zoltan@math-stat.unibe.ch
- Mario Bonk
- Affiliation: Department of Mathematics, University of Jyväskylä, P.O. Box 35, SF-40351 Jyväskylä, Finland, and Inst. für Analysis, Tech. Univ. Braunschweig, 38106 Braunschweig, Germany
- MR Author ID: 39235
- Email: M.Bonk@tu-bs.de
- Received by editor(s): April 10, 1997
- Received by editor(s) in revised form: June 29, 1997
- Additional Notes: The first author was supported by the Finnish Mathematical Society.
The second author was supported by TMR fellowship ERBFMBICT 961462. - Communicated by: Albert Baernstein II
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 801-804
- MSC (1991): Primary 30C85
- DOI: https://doi.org/10.1090/S0002-9939-99-04565-7
- MathSciNet review: 1469396