Moduli of Continuity of Harmonic Quasiregular Mappings in Bⁿ

Abstract

We prove that ωu(δ) ≤ Cωf(δ), where B̄ → ℝn is the harmonic extension of a continuous map f:Sn-1 → ℝn, if u is a K-quasiregular map. Here C is a constant depending only on n, ωf and K and ωh denotes the modulus of continuity of h. © 2010 Springer Science+Business Media B.V.