On the distribution of harmonic measure on simply connected planar domains

Dimitrios Betsakos; Alexander Yu Solynin

doi:10.1017/s1446788700003682

On the distribution of harmonic measure on simply connected planar domains

Dimitrios Betsakos, Alexander Yu Solynin

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

For a simply connected planar domain D with 0 ∈ D and dist(0, ∂ D) = 1, let h_D(r) be the harmonic measure of ∂ D ∩ {|z| ≤ r} evaluated at 0. The function h_D (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.

Original language	English
Pages (from-to)	145-151
Number of pages	7
Journal	Journal of the Australian Mathematical Society
Volume	75
Issue number	2
DOIs	https://doi.org/10.1017/s1446788700003682
State	Published - Oct 2003

Keywords

Harmonic measure

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abstract = "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.",

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