Minimization of the conformal radius under circular cutting of a domain
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 15, Tome 254 (1998), pp. 145-164
Voir la notice de l'article provenant de la source Math-Net.Ru
Let $D$ be a simply connected domain on the complex plane such that $0\in D$. For $r>0$, let $D_r$ be the connected component of $D\cap\{z:|z|$ containing the origin. For fixed $r$, we solve the problem on minimization of the conformal radius $R(D_r;0)$ among all domains $D$ with given conformal radius $R(D;0)$. This also leads to the solution of the problem on maximization of the logarithmic capacity of the local $\varepsilon$-extension $E_\varepsilon(a)$ of $E$ among all continua $E$ with given logarithmic capacity. Here, $E_\varepsilon(a)=E\cup{z:|z-a|\le\varepsilon}, a\in E,\varepsilon>0$.
@article{ZNSL_1998_254_a9,
author = {A. Yu. Solynin},
title = {Minimization of the conformal radius under circular cutting of a domain},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {145--164},
publisher = {mathdoc},
volume = {254},
year = {1998},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1998_254_a9/}
}
A. Yu. Solynin. Minimization of the conformal radius under circular cutting of a domain. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 15, Tome 254 (1998), pp. 145-164. http://geodesic.mathdoc.fr/item/ZNSL_1998_254_a9/