Abstract:
Given a complex number $\lambda\ne0,1$, we consider local homeomorphisms of a domain $D\subset\overline{\mathbb C}$ that, in a neighborhood of every point, change slightly (with a given smallness parameter $\delta$) the cross-ratio of tetrads with fixed cross-ratio $\lambda$. We prove the quasiconformality of these mappings and obtain bounds for the coefficient of quasiconformality tending to 1 as $\delta\to0$.
Keywords:cross-ratio, Möbius mapping, quasiconformal mapping, coefficient of quasiconformality, criterion for the Möbius property, Möbius midpoint condition.
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