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- Title
Harmonic Measure of Arcs of Fixed Length.
- Authors
Samarasiri, S.; Solynin, A. Yu.
- 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.
- Subjects
JORDAN; ARC length; ROTATIONAL symmetry
- Publication
Journal of Mathematical Sciences, 2022, Vol 261, Issue 6, p826
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-022-05791-2