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Dal'nevost. Mat. Zh., 2000, Volume 1, Number 1, Pages 3–7 (Mi dvmg72)  

This article is cited in 1 scientific paper (total in 1 paper)

On three disjoint domains

L. V. Kovalev

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences

Abstract: The paper deals with the following problem, stated in [Zbl.830.30014] by V. N. Dubinin and earlier, in different form, by G. P. Bakhtina [Zbl.585.30027]. Let $a_0=0$, $|a_1|=…=|a_n|=1$, $a_k\in B_k\in\overline{\mathbb C}$, where $B_0,…,B_n$ are disjoint domains, and $B_1,…,B_n$ are symmetric about the unit circle. Find the exact upper bound for $\prod_{k=0}^n r(B_k,a_k)$, where $r(B_k,a_k)$ is the inner radius radius of $B_k$ with respect to $a_k$. For $n\ge3$ this problem was recently solved by the author. In the present paper, it is solved for $n=2$.

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Document Type: Article
UDC: 517.54
MSC: 30C75
Received: 12.04.2000

Citation: L. V. Kovalev, “On three disjoint domains”, Dal'nevost. Mat. Zh., 1:1 (2000), 3–7

Citation in format AMSBIB
\Bibitem{Kov00}
\by L.~V.~Kovalev
\paper On three disjoint domains
\jour Dal'nevost. Mat. Zh.
\yr 2000
\vol 1
\issue 1
\pages 3--7
\mathnet{http://mi.mathnet.ru/dvmg72}
\elib{http://elibrary.ru/item.asp?id=5019944}


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    This publication is cited in the following articles:
    1. A. K. Bakhtin, I. V. Denega, “Sharp estimates of products of inner radii of non-overlapping domains in the complex plane”, Probl. anal. Issues Anal., 8(26):1 (2019), 17–31  mathnet  crossref
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