V. V. Aseev, T. A. Kergilova, “Anharmonic ratio and the minimal criteria for Möbius property”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2012, Volume 12, Issue 1,Pages <nobr>14

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Anharmonic ratio and the minimal criteria for Möbius property

V. V. Aseev^a, T. A. Kergilova^b

^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.

UDC: 517.54

Received: 11.10.2011