Geodesic
Normal families of light mappings of the sphere onto itself
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 733-742.

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Considering the class ${\mathcal D}$ of all continuous light mappings of the Riemann sphere $\bar{\mathbf C}$ onto itself, we introduce the notion of ${\mathcal D}$-normal family and prove that every mapping $f$ from a given Möbius invariant and ${\mathcal D}$-normal family ${\mathcal F}\subset {\mathcal D}$ is a composition of a $K$-quasiconformal automorphism of $\bar{\mathbf C}$ with the mapping, realized by a meromorphic function on $\bar{\mathbf C}$, where a constant $K$ is common for all $f\in {\mathcal F}$.
Keywords: quasiconformal mapping, mapping of bounded distortion, quasimeromorphic mapping, normal family, Möbius mapping, Möbius invariant family, Stoilov theorem, light mapping, open mapping.
Mots-clés : graph convergence 
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V. V. Aseev; D. G. Kuzin. Normal families of light mappings of the sphere onto itself. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 733-742. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a60/

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