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Zapiski Nauchnykh Seminarov LOMI, 1981, Volume 112, Pages 172–183 (Mi znsl3937)  

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
Full-text PDF (526 kB) Citations (8)
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.
English version:
Journal of Soviet Mathematics, 1984, Volume 25, Issue 2, Pages 1093–1101
DOI: https://doi.org/10.1007/BF01680833
Bibliographic databases:
Document Type: Article
UDC: 517.54
Language: Russian
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
Citation in format AMSBIB
\Bibitem{Fed81}
\by S.~I.~Fedorov
\paper Maximum of a~conformal invariant in the problem of nonoverlapping domains
\inbook Analytical theory of numbers and theory of functions. Part~4
\serial Zap. Nauchn. Sem. LOMI
\yr 1981
\vol 112
\pages 172--183
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl3937}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=644003}
\zmath{https://zbmath.org/?q=an:0531.30025|0483.30013}
\transl
\jour J. Soviet Math.
\yr 1984
\vol 25
\issue 2
\pages 1093--1101
\crossref{https://doi.org/10.1007/BF01680833}
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  • https://www.mathnet.ru/eng/znsl/v112/p172
  • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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