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Proceedings of the American Mathematical Society

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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

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