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

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Problems on extremal decomposition in families of systems of nonoverlapping simply connected domains in the presence of a high degree of symmetry in the problem conditions are investigated. Bibliography: 12 titles.

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References

  1. G. V. Kuz’mina, “Methods in geoometric function theory. II,” Algebra Analiz, 9, No. 5, 1–50 (1997).

    MathSciNet  Google Scholar 

  2. V. N. Dubinin, “Symmetrization in the geometric theory of functions of a complex variable,” Usp. Mat. Nauk, 49, No. 1, 1–76 (1994).

    MathSciNet  MATH  Google Scholar 

  3. V. N. Dubinin, Capacities of Condensers and Symmetrization in the Geometric Theory of Functions of a Complex Variable [in Russian], Vladivostok (2009).

  4. E. G. Emel’yanov, “On the problem on maximizing the product of powers of conformal radii of nonoverlapping domains,” Zap. Nauchn. Semin. POMI, 286, 103–114 (2002).

    MathSciNet  Google Scholar 

  5. E. G. Emel’yanov, “Conformal invariant functionals on the Riemann sphere,” Zap. Nauchn. Semin. POMI, 276, 134–154 (2001).

    Google Scholar 

  6. G. V. Kuz’mina, “On the problem of maximum of the product of conformal radii of nonoverlapping domains,” Zap. Nauchn. Semin. POMI, 100, 131–145 (1980).

    MathSciNet  MATH  Google Scholar 

  7. S. I. Fedorov, “On the maximum of a conformal invariant in the problem on nonoverlapping domains,” Zap. Nauchn. Semin. POMI, 112, 172–183 (1981).

    MATH  Google Scholar 

  8. G. V. Kuz’mina, “On the question of extremal decomposition of the Riemann sphere,” Zap. Nauchn. Semin. POMI, 185, 72–95 (1090).

    Google Scholar 

  9. G. V. Kuz’man, “Modules of families of curves and quadratic differentials,” Tr. Mat. Inst. Steklova, 139, 1–243 (1980).

    Google Scholar 

  10. E. G. Emel’yanov, “On problems of extremal decomposition,” Zap. Nauchn. Semin. POMI, 154, 76–89 (1986).

    MATH  Google Scholar 

  11. A. Yu. Solynin, “Modules and extremal metric problems,” Algebra Analiz, 11, No. 1, 3–86 (1999).

    MathSciNet  Google Scholar 

  12. L. I. Kolbina, “Some extremal problems in conformal mapping,” Dokl. Akad. Nauk SSSR, 84, 865–868 (1952).

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    G. V. Kuz’mina

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  1. G. V. Kuz’mina
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Correspondence to G. V. Kuz’mina.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 392, 2011, pp. 146–158.

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Kuz’mina, G.V. Problems on the maximum of a conformal invariant in the presence of a high degree of symmetry. J Math Sci 184, 746–752 (2012). https://doi.org/10.1007/s10958-012-0895-z

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  • DOI: https://doi.org/10.1007/s10958-012-0895-z

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