Stöılow factorization for quasiregular mappings in all dimensions

Abstract. We generalize to higher dimensions the classical Stöılow factori-sation theorem; we show that any quasiregular mapping f of the Riemann n-sphere R̂n ≈ Sn can be written in the form f = ϕ ◦ h, where h: Sn → Sn is quasiconformal and ϕ is a uniformly quasiregular mapping, hence rational with respect to some bounded measurable conformal structure. 1