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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 1(9), Pages 110–123 (Mi msb2020)  

This article is cited in 6 scientific papers (total in 6 papers)

The symmetrization method in problems on nonoverlapping domains

V. N. Dubinin


Abstract: A new approach to the use of symmetrization is considered. Sterner symmetrization is taken as the main tool. An arbitrary symmetrization transformation connected with a given quadratic differential $Q(z)dz^2$ is obtained by successive application of the mappng $\zeta=\int Q^{1/2}(z) dz$ and Steiner symmetrization.
As a consequence of the main theorem, the corresponding results of Lavrent'ev, Goluzin, Jenkins, and others are refined and generalized to the case of domains of arbitrary connectivity (not necessarily having a filling).
Bibliography: 21 titles.

Full text: PDF file (771 kB)
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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 107–119

Bibliographic databases:

UDC: 517.54
MSC: Primary 30C20, 30C55; Secondary 30C25, 30C85, 30F30, 31A15
Received: 31.05.1984

Citation: V. N. Dubinin, “The symmetrization method in problems on nonoverlapping domains”, Mat. Sb. (N.S.), 128(170):1(9) (1985), 110–123; Math. USSR-Sb., 56:1 (1987), 107–119

Citation in format AMSBIB
\Bibitem{Dub85}
\by V.~N.~Dubinin
\paper The symmetrization method in problems on nonoverlapping domains
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 1(9)
\pages 110--123
\mathnet{http://mi.mathnet.ru/msb2020}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=805698}
\zmath{https://zbmath.org/?q=an:0604.30026|0588.30024}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 107--119
\crossref{https://doi.org/10.1070/SM1987v056n01ABEH003026}


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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, “Symmetrization in the geometric theory of functions of a complex variable”, Russian Math. Surveys, 49:1 (1994), 1–79  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. L. V. Kovalev, “On the inner radii of symmetric nonoverlapping domains”, Russian Math. (Iz. VUZ), 44:6 (2000), 77–78  mathnet  mathscinet  zmath  elib
    3. L. V. Kovalev, “O trekh neperesekayuschikhsya oblastyakh”, Dalnevost. matem. zhurn., 1:1 (2000), 3–7  mathnet  elib
    4. [Anonymous], “Moduli on Teichmüller Spaces”, Moduli of Families of Curves for Conformal and Quasconformal Mapping, Lecture Notes in Mathematics, 1788, Springer-Verlag Berlin, 2002, 175–206  isi
    5. V. N. Dubinin, D. A. Kirillova, “On extremal decomposition problems”, J. Math. Sci. (N. Y.), 157:4 (2009), 573–583  mathnet  crossref  zmath
    6. V. N. Dubinin, “Quadratic forms involving Green's and Robin functions”, Sb. Math., 200:10 (2009), 1439–1452  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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