Abstract:
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 $\bar{R}^n$.
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