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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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


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.
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Additional Information
  • Zoltan Balogh
  • Affiliation: Universität Bern, Mathematisches Institut, Sidlerstr. 5, CH-3012 Bern, Switzerland
  • Email:
  • 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:
  • 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:
  • MathSciNet review: 1469396