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Proceedings of the American Mathematical Society

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Lengths of radii under conformal maps
of the unit disc

Authors: Zoltan Balogh and Mario Bonk
Journal: Proc. Amer. Math. Soc. 127 (1999), 801-804
MSC (1991): Primary 30C85
MathSciNet review: 1469396
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

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Additional Information

Zoltan Balogh
Affiliation: Universität Bern, Mathematisches Institut, Sidlerstr. 5, CH-3012 Bern, Switzerland

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

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
Article copyright: © Copyright 1999 American Mathematical Society