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Zap. Nauchn. Sem. POMI, 2011, Volume 392, Pages 146–158 (Mi znsl4582)  

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

Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry

G. V. Kuz'mina

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia

Abstract: The problem on the maximum of the conformal invariant
$$ 2\pi\sum_{k=1}^nM(D_k,a_k)-\frac2{n-1}\prod_{1\leq k<l\leq n}|a_k-a_l|, $$
for all systems of points $\{a_1,…,a_n\}$ and all systems $\{D_1,…,D_n\}$ of nonoverlapping simply connected domains satisfying the condition $a_k\in D_k$, $k=1,…,n$, is investigated. Here $M(D,a)$ is the reduced module of a domain $D$ with respect to a point $a\in D $. It is assumed that $n$ is even and systems of points $a_1,…,a_n$ under consideration have a high degree of symmetry.

Key words and phrases: reduced module of a domain, conformal radius of a domain, conformal invariant.

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English version:
Journal of Mathematical Sciences (New York), 2012, 184:6, 746–752

Document Type: Article
UDC: 511.3
Received: 30.09.2011

Citation: G. V. Kuz'mina, “Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry”, Analytical theory of numbers and theory of functions. Part 26, Zap. Nauchn. Sem. POMI, 392, POMI, St. Petersburg, 2011, 146–158; J. Math. Sci. (N. Y.), 184:6 (2012), 746–752

Citation in format AMSBIB
\Bibitem{Kuz11}
\by G.~V.~Kuz'mina
\paper Problems on the maximum of a~conformal invariant in the presence of a~high degree of symmetry
\inbook Analytical theory of numbers and theory of functions. Part~26
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 392
\pages 146--158
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4582}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2012
\vol 184
\issue 6
\pages 746--752
\crossref{https://doi.org/10.1007/s10958-012-0895-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864286744}


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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 222:5 (2017), 645–689  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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