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Zapiski Nauchnykh Seminarov LOMI, 1981, Volume 112, Pages 172–183
(Mi znsl3937)
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This article is cited in 8 scientific papers (total in 8 papers)
Maximum of a conformal invariant in the problem of nonoverlapping domains
S. I. Fedorov
Abstract:
The paper is devoted to the well-known circle of problems on the maximum of the products of powers of conformal radii of nonoverlapping domains. Let $a_1,\dots,a_n$ be distinct points of $\mathbb C$ and let $D_1,\dots,D_n$ be a system of simply connected domains in $\overline{\mathbb C}$, pairwise disjoint and such that $a_k\in D_k$, $k=1,\dots,n$. By $R(D_k,a_k)$ we denote the conformal radius of the domain $D_k$ relative to the point $a_k$. One considers the problem on the maximum of the product
$$
\prod^n_{k=1}R(D_k,a_k)\Bigl\{\prod_{1\le k<l\le n}|a_k-a_l|\Bigr\}^{-2/(n-1)}
$$
in the family of all indicated systems of domains, under the condition that $a_1,\dots,a_n$ runs over all systems of distinct points in $\mathbb C$ ($n\ge4$) and one finds the geometric characteristic of the extremal configurations of this problem in terms of the associated quadratic differential.
Citation:
S. I. Fedorov, “Maximum of a conformal invariant in the problem of nonoverlapping domains”, Analytical theory of numbers and theory of functions. Part 4, Zap. Nauchn. Sem. LOMI, 112, "Nauka", Leningrad. Otdel., Leningrad, 1981, 172–183; J. Soviet Math., 25:2 (1984), 1093–1101
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https://www.mathnet.ru/eng/znsl3937 https://www.mathnet.ru/eng/znsl/v112/p172
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Abstract page: | 114 | Full-text PDF : | 52 |
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