Geodesic
The coefficient of quasim\"obiusness in Ptolemaic spaces
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 246-257.

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In ptolemaic spaces the class of $\eta$-quasimöbius mappings $f: X\to Y$ with control function $\eta(t)= C \max\{ t^{\alpha}, t^{1/\alpha}\}$ may be completely characterized by the inequality $ K^{-1}\leq (1 + \log P(fT))/(1+ \log P(T)) \leq K$ for all tetrads $T\subset X$ where $P(T)$ denotes the ptolemaic characteristic of a tetrad. The number $K$ has properties quite similar to those of coefficients of quasiconformality, so the concept of $K$-quasimöbius mapping may be introduced. In particular, the stability theorem is proved for $(1+\varepsilon)$-quasimöbius mappings in $\bar{R}^n$.
Keywords: Möbius mapping, quasimöbius mapping, (power) quasimöbius mapping, quasisymmetric mapping, stability theorem.
Mots-clés : ptolemaic space 
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V. V. Aseev. The coefficient of quasim\"obiusness in Ptolemaic spaces. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 246-257. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a123/

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