RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
 General information Latest issue Archive Impact factor Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Dal'nevost. Mat. Zh.: Year: Volume: Issue: Page: Find

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

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 $n=2$.

Full text: PDF file (161 kB)
References: PDF file   HTML file

Document Type: Article
UDC: 517.54
MSC: 30C75

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}