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Zap. Nauchn. Sem. POMI, 2008, Volume 357, Pages 54–74 (Mi znsl2119)  

This article is cited in 7 scientific papers (total in 7 papers)

On extremal decomposition problems

V. N. Dubinina, D. A. Kirillovab

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
b Far-Eastern State Social-Humanitarian Academy

Abstract: We adapt the capacity approach and symmetrization method to some extremal decomposition problems on the disk unit or an annulus. We consider the problems on the maximum product of the inner radii of pairwise disjoint domains and the maximum product of the Robin radii of such domains. The new invariants with respect to Möbius transformations of the Riemann sphere are introduced. In particular, for these invariants the problems on extremal decomposition with free poles on the unit circle are investigated. Bibl. – 19 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 157:4, 573–583

Bibliographic databases:

UDC: 517.54
Received: 01.10.2008

Citation: V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, Analytical theory of numbers and theory of functions. Part 23, Zap. Nauchn. Sem. POMI, 357, POMI, St. Petersburg, 2008, 54–74; J. Math. Sci. (N. Y.), 157:4 (2009), 573–583

Citation in format AMSBIB
\Bibitem{DubKir08}
\by V.~N.~Dubinin, D.~A.~Kirillova
\paper On extremal decomposition problems
\inbook Analytical theory of numbers and theory of functions. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 357
\pages 54--74
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2119}
\zmath{https://zbmath.org/?q=an:1182.30036}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 157
\issue 4
\pages 573--583
\crossref{https://doi.org/10.1007/s10958-009-9342-1}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. V. Kuz'mina, “On symmetric configurations in some problems on extremal decomposition. II”, J. Math. Sci. (N. Y.), 157:4 (2009), 632–645  mathnet  crossref  zmath
    2. D. A. Kirillova, “O maksimume mebiusova invarianta v zadache s chetyrmya nenalegayuschimi oblastyami”, Dalnevost. matem. zhurn., 10:1 (2010), 41–49  mathnet  elib
    3. V. N. Dubinin, D. A. Kirillova, “Nekotorye primeneniya ekstremalnykh razbienii v geometricheskoi teorii funktsii”, Dalnevost. matem. zhurn., 10:2 (2010), 130–152  mathnet  elib
    4. G. V. Kuz'mina, “The method of extremal metric in the problem on the maximum of a conformal invariant”, J. Math. Sci. (N. Y.), 178:2 (2011), 187–197  mathnet  crossref
    5. E. G. Prilepkina, “On composition principles for reduced moduli”, Siberian Math. J., 52:6 (2011), 1079–1091  mathnet  crossref  mathscinet  isi
    6. J. Math. Sci. (N. Y.), 222:5 (2017), 645–689  mathnet  crossref  mathscinet
    7. S. I. Kalmykov, E. G. Prilepkina, “On the $p$-harmonic Robin radius in the Euclidean space”, J. Math. Sci. (N. Y.), 225:6 (2017), 969–979  mathnet  crossref  mathscinet
  • Записки научных семинаров ПОМИ
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