Hostname: page-component-8448b6f56d-dnltx Total loading time: 0 Render date: 2024-04-23T14:47:18.740Z Has data issue: false hasContentIssue false
  • English
  • Français

On the distribution of harmonic measure on simply connected planar domains

Published online by Cambridge University Press:  09 April 2009

Dimitrios Betsakos  and
Alexander Yu. Solynin
Dimitrios Betsakos
Affiliation:
Department of Mathematics Aristotle University of Thessaloniki54124 ThessalonikiGreece e-mail: betsakos@auth.gr
Alexander Yu. Solynin
Affiliation:
Steklov Mathematical InstituteSt. Petersburg Branch Russian Academy of Sciences Fontanka 27 191011 St. PetersburgRussia e-mail: solynin@pdmi.ras.ru
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

For a simply connected planar domain D with 0 ∈ D and dist(0, ∂D) = 1, let hD(r) be the harmonic measure of ∂ D ∩{|Z| ≤ r} evaluated at 0. The function hD(r) is the distribution of harmonic measure. It has been studied by B. L. Walden and L. A. Ward. We continue their study and answer some questions raised by them by constructing domains with pre-specified distribution.

Keywords

harmonic measure
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 2 , October 2003 , pp. 145 - 152
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Betsakos, D., ‘Harmonic measure on simply connected domains of fixed inradius’, Ark. Mat. 36 (1998), 275–306.Google Scholar
[2]Betsakos, D., ‘Geometric theorems and problems for harmonic measure’, Rocky Mountain J. Math. 31 (2001), 773–795.CrossRefGoogle Scholar
[3]Tsuji, M., Potential theory in modern function theory (Maruzen, Tokyo, 1959).Google Scholar
[4]Walden, B. L. and Ward, L. A., ‘Distributions of harmonic measure for planar domains’, in: XVIth Rolf Nevanlinna Colloquium (Joensuu 1995) (de Gruyter, Berlin, 1996) pp. 289–299.Google Scholar
[5]Walden, B. L. and Ward, L. A., ‘Asymptotic behaviour of distributions of harmonic measure for planar domains’, Complex Variables Theory Appl. 46 (2001), 157–177.Google Scholar