Harmonic Measure of Arcs of Fixed Length

S. Samarasiri, A. Yu Solynin

Research output: Contribution to journalArticlepeer-review

Abstract

We consider Jordan domains Ω with piece-wise smooth boundaries such that all arcs α ⊂ ∂Ω having fixed length l, 0 < l < length(∂Ω), have equal harmonic measures ω(z0, α, Ω) evaluated at some point z0 ∈ Ω. It is proved that Ω is a disk centered at z0 if the ratio l/length(∂Ω) is irrational and that Ω possesses rotational symmetry by some angle 2π/n, n ≥ 2, around the point z0, if this ratio is rational.

Original languageEnglish
Pages (from-to)826-831
Number of pages6
JournalJournal of Mathematical Sciences (United States)
Volume261
Issue number6
DOIs
StatePublished - Mar 2022

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