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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2012, Volume 12, Issue 1, Pages 14–28
(Mi vngu107)
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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
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
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
Linking options:
https://www.mathnet.ru/eng/vngu107 https://www.mathnet.ru/eng/vngu/v12/i1/p14
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Abstract page: | 235 | Full-text PDF : | 143 | References: | 50 | First page: | 1 |
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