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Mat. Sb. (N.S.), 1970, Volume 83(125), Number 2(10), Pages 261–272 (Mi msb3512)  

This article is cited in 19 scientific papers (total in 19 papers)

The modulus method for nonhomeomorphic quasiconformal mappings

E. A. Poletskii


Abstract: The modulus method is one of the most effective methods in the theory of quasiconformal homeomorphisms. Over the course of a long time there has been no success, however, in applying this method to the analysis of nonhomeomorphic quasiconformal mappings of spatial domains.
In the present paper inequalities are established for the moduli of families of curves corresponding with each other under a certain, not necessarily homeomorphic, quasiconformal mapping. These inequalities are applied to the study of the relation of dilatation with the minimal multiplicity of a ramification of such mappings.
Bibliography: 7 titles.

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English version:
Mathematics of the USSR-Sbornik, 1970, 12:2, 260–270

Bibliographic databases:

UDC: 517.54
MSC: 30C65, 30C20, 30C35
Received: 03.02.1970

Citation: E. A. Poletskii, “The modulus method for nonhomeomorphic quasiconformal mappings”, Mat. Sb. (N.S.), 83(125):2(10) (1970), 261–272; Math. USSR-Sb., 12:2 (1970), 260–270

Citation in format AMSBIB
\Bibitem{Pol70}
\by E.~A.~Poletskii
\paper The modulus method for nonhomeomorphic quasiconformal mappings
\jour Mat. Sb. (N.S.)
\yr 1970
\vol 83(125)
\issue 2(10)
\pages 261--272
\mathnet{http://mi.mathnet.ru/msb3512}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=274753}
\zmath{https://zbmath.org/?q=an:0207.37603}
\transl
\jour Math. USSR-Sb.
\yr 1970
\vol 12
\issue 2
\pages 260--270
\crossref{https://doi.org/10.1070/SM1970v012n02ABEH000921}


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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. E. A. Poletskii, “On the removal of singularities of quasiconformal mappings”, Math. USSR-Sb., 21:2 (1973), 240–254  mathnet  crossref  mathscinet  zmath
    2. S. K. Vodop'yanov, “Closure of Classes of Mappings with Bounded Distortion on Carnot Groups”, Siberian Adv. Math., 14:1 (2004), 84–125  mathnet  mathscinet  zmath  elib
    3. A. N. Malyutina, M. A. Elizarova, “Otsenki iskazheniya modulei dlya otobrazhenii s $s$-usrednennoi kharakteristikoi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2010, no. 2(10), 5–15  mathnet  elib
    4. E. A. Sevost'yanov, “On the branch points of mappings with the unbounded coefficient of quasiconformality”, Siberian Math. J., 51:5 (2010), 899–912  mathnet  crossref  mathscinet  isi  elib
    5. E. A. Sevostyanov, “About space mappings with integral restrictions on the characteristics”, St. Petersburg Math. J., 24:1 (2013), 99–115  mathnet  crossref  mathscinet  zmath  isi  elib
    6. E. A. Sevost'yanov, “On the local behavior of mappings with unbounded quasiconformality coefficient”, Siberian Math. J., 53:3 (2012), 520–531  mathnet  crossref  mathscinet  isi
    7. A. N. Malyutina, M. A. Elizarova, “Ob ekvivalentnosti analiticheskogo i geometricheskogo opredelenii otobrazhenii s $s$-usrednennoi kharakteristikoi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2014, no. 1(27), 25–41  mathnet
    8. Vodop'yanov S.K., “On the Regularity of the Poletskii Function Under Weak Analytic Assumptions on the Given Mapping”, Dokl. Math., 89:2 (2014), 157–161  crossref  mathscinet  zmath  isi
    9. E. A. Sevostyanov, D. S. Dolya, “O ravnostepennoi nepreryvnosti odnogo semeistva prostranstvennykh otobrazhenii s neogranichennoi kharakteristikoi”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2014, no. 3(22), 41–55  mathnet
    10. A. N. Baykin, S. K. Vodop'yanov, “Capacity estimates, Liouville's theorem, and singularity removal for mappings with bounded $(p,q)$-distortion”, Siberian Math. J., 56:2 (2015), 237–261  mathnet  crossref  mathscinet  isi  elib  elib
    11. M. V. Tryamkin, “Modulus inequalities for mappings with weighted bounded $(p,q)$-distortion”, Siberian Math. J., 56:6 (2015), 1114–1132  mathnet  crossref  crossref  mathscinet  isi  elib
    12. M. V. Tryamkin, “Otsenki na moduli semeistv krivykh dlya otobrazhenii s vesovym ogranichennym $(p,q)$-iskazheniem”, Vladikavk. matem. zhurn., 17:3 (2015), 65–74  mathnet
    13. D. P. Il'yutko, E. A. Sevost'yanov, “Open discrete mappings with unbounded coefficient of quasi-conformality on Riemannian manifolds”, Sb. Math., 207:4 (2016), 537–580  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. A. N. Malyutina, K. A. Alipova, “K voprosu o granichnykh svoistvakh prostranstvennykh negomeomorfnykh otobrazhenii s $s$-usrednennoi kharakteristikoi”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2016, no. 3(41), 16–30  mathnet  crossref  elib
    15. Sevost'yanov E., “On local behavior of mappings with unbounded characteristic”, Lobachevskii J. Math., 38:2, SI (2017), 371–378  crossref  mathscinet  zmath  isi  scopus
    16. S. K. Vodopyanov, “Basics of the quasiconformal analysis of a two-index scale of spatial mappings”, Siberian Math. J., 59:5 (2018), 805–834  mathnet  crossref  crossref  isi  elib
    17. S. K. Vodopyanov, “Differentiability of mappings of the Sobolev space $W^1_{n-1}$ with conditions on the distortion function”, Siberian Math. J., 59:6 (2018), 983–1005  mathnet  crossref  crossref  isi  elib
    18. Vodopyanov S.K., “Foundations of Quasiconformal Analysis of a Two-Index Scale of Spatial Mappings”, Dokl. Math., 99:1 (2019), 23–27  crossref  zmath  isi
    19. D. P. Ilyutko, E. A. Sevost'yanov, “Boundary behaviour of open discrete mappings on Riemannian manifolds. II”, Sb. Math., 211:4 (2020), 539–582  mathnet  crossref  crossref
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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