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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 1, Pages 14–28 (Mi vngu107)  
This article is cited in 1 scientific paper (total in 1 paper)

Anharmonic ratio and the minimal criteria for Möbius property

V. V. Aseeva, T. A. Kergilovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
b Gorno-Altaisk State University, Gorno-Altaisk, Russia
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Abstract: We give some criteria for Möbius property of a homeomorphism of domains in $\bar R^n$ which preserves fixed anharmonic ratio $\lambda\neq0,1,\infty$. For the case of even-dimensional space as well as for the case of real $\lambda$ the requirement of a map to be homeomorphism in the theorem can be replaced by injectivity and Borel measurability. For a homeomorphism which slightly changes fixed cross-ratio we get the upper estimates for it's coefficient of quasiconformality.
Keywords: anharmonic ratio, Möbius mapping, geometric criteria of Möbius property, quasiconformal mapping, coefficient of quasiconformality.
Received: 11.10.2011
English version:
Journal of Mathematical Sciences, 2014, Volume 198, Issue 5, Pages 485–497
DOI: https://doi.org/10.1007/s10958-014-1804-4
Document Type: Article
UDC: 517.54
Language: Russian
Citation: V. V. Aseev, T. A. Kergilova, “Anharmonic ratio and the minimal criteria for Möbius property”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 12:1 (2012), 14–28; J. Math. Sci., 198:5 (2014), 485–497
Citation in format AMSBIB
\Bibitem{AseKer12}
\by V.~V.~Aseev, T.~A.~Kergilova
\paper Anharmonic ratio and the minimal criteria for M\"obius property
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2012
\vol 12
\issue 1
\pages 14--28
\mathnet{http://mi.mathnet.ru/vngu107}
\transl
\jour J. Math. Sci.
\yr 2014
\vol 198
\issue 5
\pages 485--497
\crossref{https://doi.org/10.1007/s10958-014-1804-4}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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