Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 4, pp. 375-379
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V. Azarin; A. Gol'dberg. A sharp inequality for the order of the minimal positive harmonic function in $T$-homogeneous domain. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 11 (2004) no. 4, pp. 375-379. http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a0/
@article{JMAG_2004_11_4_a0,
author = {V. Azarin and A. Gol'dberg},
title = {A sharp inequality for the order of the minimal positive harmonic function in $T$-homogeneous domain},
journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
pages = {375--379},
year = {2004},
volume = {11},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a0/}
}
TY - JOUR
AU - V. Azarin
AU - A. Gol'dberg
TI - A sharp inequality for the order of the minimal positive harmonic function in $T$-homogeneous domain
JO - Žurnal matematičeskoj fiziki, analiza, geometrii
PY - 2004
SP - 375
EP - 379
VL - 11
IS - 4
UR - http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a0/
LA - en
ID - JMAG_2004_11_4_a0
ER -
%0 Journal Article
%A V. Azarin
%A A. Gol'dberg
%T A sharp inequality for the order of the minimal positive harmonic function in $T$-homogeneous domain
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2004
%P 375-379
%V 11
%N 4
%U http://geodesic.mathdoc.fr/item/JMAG_2004_11_4_a0/
%G en
%F JMAG_2004_11_4_a0
Let $G$ be a simply connected domain in $\mathbb C$ which is $T$-homoheneous, i.e., $TG=G$ for some $T>0$. Let $\rho(G)$ be the order of the minimal positive harmonic function in $G$. We prove that a kind of symmetrization of $G$ and prove that it does not increase $\rho(G)$. This implies a sharp lower bound for $\rho(G)$ in terms of conformal modulus of a quadrilateral naturally connected with $G$.
