TY - JOUR
T1 - Harmonic Measure of Arcs of Fixed Length
AU - Samarasiri, S.
AU - Solynin, A. Yu
N1 - Publisher Copyright:
© 2022, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2022/3
Y1 - 2022/3
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85128962101&partnerID=8YFLogxK
U2 - 10.1007/s10958-022-05791-2
DO - 10.1007/s10958-022-05791-2
M3 - Article
AN - SCOPUS:85128962101
VL - 261
SP - 826
EP - 831
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 6
ER -