Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30C85

Retrieve articles in all journals with MSC (1991): 30C85


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
Email: M.Bonk@tu-bs.de

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04565-7
PII: S 0002-9939(99)04565-7
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