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Mat. Sb., 2015, Volume 206, Number 1, Pages 69–96 (Mi msb8309)  

This article is cited in 10 scientific papers (total in 10 papers)

Circular symmetrization of condensers on Riemann surfaces

V. N. Dubininab

a Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences, Vladivostok
b Far Eastern Federal University, Vladivostok

Abstract: We give a simplified definition of the new version of circular symmetrization which has previously been suggested by the author for solving extremal problems in geometric function theory. A proof of the symmetrization principle for the capacities of condensers on Riemann surfaces is presented. In addition, the class of condensers under consideration is extended and all the cases of equality in the symmetrization principle are found.
Bibliography: 22 titles.

Keywords: circular symmetrization, condenser capacity, Riemann surface, Chebyshev polynomial.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022
This work was supported by the Russian Science Foundation under grant no. 14-11-00022.


DOI: https://doi.org/10.4213/sm8309

Full text: PDF file (656 kB)
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English version:
Sbornik: Mathematics, 2015, 206:1, 61–86

Bibliographic databases:

UDC: 517.54
MSC: 30A10, 30C55, 30C85
Received: 26.11.2013

Citation: V. N. Dubinin, “Circular symmetrization of condensers on Riemann surfaces”, Mat. Sb., 206:1 (2015), 69–96; Sb. Math., 206:1 (2015), 61–86

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Dubinin, “Inequalities for moduli of the circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 207:6 (2015), 832–838  mathnet  crossref
    2. V. N. Dubinin, “Distortion theorems for circumferentially mean $p$-valent functions”, J. Math. Sci. (N. Y.), 217:1 (2016), 28–36  mathnet  crossref  mathscinet  elib
    3. V. N. Dubinin, “An Extremal Problem for the Derivative of a Rational Function”, Math. Notes, 100:5 (2016), 714–719  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. N. Dubinin, “Critical values and moduli of derivative of a complex polynomial at its zeros”, J. Math. Sci. (N. Y.), 225:6 (2017), 877–882  mathnet  crossref  mathscinet
    5. P. A. Pugach, V. A. Shlyk, “Сondensers and equivalent open sets on a Riemann surface”, J. Math. Sci. (N. Y.), 225:6 (2017), 994–1011  mathnet  crossref  mathscinet
    6. V. N. Dubinin, “The logarithmic energy of zeros and poles of a rational function”, Siberian Math. J., 57:6 (2016), 981–986  mathnet  crossref  crossref  isi  elib
    7. P. Pugach, V. Shlyk, “Moduli, capacity, BV-functions on the Riemann surfaces”, Lobachevskii J. Math., 38:2 (2017), 338–351  crossref  mathscinet  zmath  isi  scopus
    8. V. N. Dubinin, “Poyas lemniskat i teoremy iskazheniya dlya mnogolistnykh funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 33, Posvyaschaetsya pamyati Galiny Vasilevny KUZMINOI, Zap. nauchn. sem. POMI, 458, POMI, SPb., 2017, 17–30  mathnet
    9. V. N. Dubinin, “Lemniscate Zone and Distortion Theorems for Multivalent Functions. II”, Math. Notes, 104:5 (2018), 683–688  mathnet  crossref  crossref  isi  elib
    10. V. N. Dubinin, “Distortion theorem for complex polynomials”, Sib. elektron. matem. izv., 15 (2018), 1410–1415  mathnet  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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