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Sibirsk. Mat. Zh., 2010, Volume 51, Number 5, Pages 1129–1146 (Mi smj2151)  

This article is cited in 16 scientific papers (total in 16 papers)

On the branch points of mappings with the unbounded coefficient of quasiconformality

E. A. Sevost'yanov

Institute of Applied Mathematics and Mechanics, Donetsk, Ukraine

Abstract: We study relations between the quantity characterizing the distortion of families of curves under a given mapping and the structure of the branch point set of this mapping. For $n\ge3$ we establish that the image of the branch point set of an open discrete mapping with an isolated essential singularity is an unbounded set in $\mathbb R^n$ provided that the mapping satisfies certain geometric conditions controlling the distortion of concentric annuli centered at this point.

Keywords: mapping with bounded distortion, mapping with finite distortion, modulus of a family of curves.

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English version:
Siberian Mathematical Journal, 2010, 51:5, 899–912

Bibliographic databases:

UDC: 517.5
Received: 30.11.2008
Revised: 07.05.2010

Citation: E. A. Sevost'yanov, “On the branch points of mappings with the unbounded coefficient of quasiconformality”, Sibirsk. Mat. Zh., 51:5 (2010), 1129–1146; Siberian Math. J., 51:5 (2010), 899–912

Citation in format AMSBIB
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\paper On the branch points of mappings with the unbounded coefficient of quasiconformality
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
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\pages 1129--1146
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\yr 2010
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\pages 899--912
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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. Sevostyanov E.A., Salimov R.R., “Analog teoremy lavrenteva - zoricha o globalnom gomeomorfizme dlya otobrazhenii s neogranichennoi kharakteristikoi”, Vestnik Volgogradskogo gosudarstvennogo universiteta. Seriya 1: Matematika. Fizika, 2011, no. 2, 80–90  elib
    2. Sevostyanov E.A., Salimov R.R., “Analog teoremy lavrenteva - zoricha o globalnom gomeomorfizme dlya otobrazhenii s neogranichennoi kharakteristikoi”, Vestnik volgogradskogo gosudarstvennogo universiteta. seriya 1: matematika. fizika, 2011, no. 2, 80–90  elib
    3. Sevost'yanov E.A., “On the Openness and Discreteness of Mappings with Unbounded Characteristic of Quasiconformality”, Ukrainian Math J, 63:8 (2012), 1298–1305  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. Sevost'yanov E.A., “On the Boundary Behavior of Open Discrete Mappings with Unbounded Characteristic”, Ukr. Math. J., 64:6 (2012), 979–984  crossref  mathscinet  zmath  isi  scopus
    6. R. R. Salimov, “Lower estimates of $p$-modulus and mappings of Sobolev's class”, St. Petersburg Math. J., 26:6 (2015), 965–984  mathnet  crossref  mathscinet  isi  elib  elib
    7. Sevost'yanov E.A., “on Equicontinuous Families of Mappings Without Values in Variable Sets”, Ukr. Math. J., 66:3 (2014), 404–414  crossref  mathscinet  zmath  isi  scopus
    8. Ryazanov V. Sevost'yanov E. Srebro U. Yakubov E., “on Equicontinuity of Ring Q-Mappings”, Anal. Math. Phys., 4:1-2, SI (2014), 145–156  crossref  mathscinet  zmath  isi  elib  scopus
    9. Cristea M., “on Generalized Quasiconformal Mappings”, Complex Var. Elliptic Equ., 59:2 (2014), 232–246  crossref  mathscinet  zmath  isi  elib  scopus
    10. Cristea M., “Local Homeomorphisms Satisfying Generalized Modular Inequalities”, Complex Var. Elliptic Equ., 59:10 (2014), 1363–1387  crossref  mathscinet  zmath  isi  elib  scopus
    11. R. R. Salimov, “O konechnoi lipshitsevosti klassov Orlicha–Soboleva”, Vladikavk. matem. zhurn., 17:1 (2015), 64–77  mathnet
    12. Golberg A. Salimov R. Sevost'yanov E., “Singularities of Discrete Open Mappings With Controlled P-Module”, J. Anal. Math., 127 (2015), 303–328  crossref  mathscinet  zmath  isi  elib  scopus
    13. Sevost'yanov E., “the Miniowitz and Vuorinen Theorems For the Mappings With Non-Bounded Characteristics”, Isr. J. Math., 209:2 (2015), 527–545  crossref  mathscinet  zmath  isi  scopus
    14. Sevost'yanov E.A., “on the Removability of Isolated Singularities of Orlicz-Sobolev Classes With Branching”, Ukr. Math. J., 68:5 (2016), 777–790  crossref  mathscinet  isi  scopus
    15. Golberg A. Salimov R. Sevost'yanov E., “Normal Families of Discrete Open Mappings With Controlled P-Module”, Complex Analysis and Dynamical Systems Vi, Pt 2: Complex Analysis, Quasiconformal Mappings, Complex Dynamics, Contemporary Mathematics, 667, ed. Agranovsky M. BenArtzi M. Galloway G. Karp L. Khavinson D. Reich S. Weinstein G. Zalcman L., Amer Mathematical Soc, 2016, 83–103  crossref  mathscinet  zmath  isi
    16. Sevost'yanov E.A., “on the Local Behavior of Open Discrete Mappings From the Orlicz-Sobolev Classes”, Ukr. Math. J., 68:9 (2017), 1447–1465  crossref  isi  scopus
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