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We prove that ω u (δ) ≤ Cω f (δ), where u : B n → R n is the harmonic extension of a continuous map f : S n−1 → R n , if u is a K-quasiregular map. Here C is a constant depending only on n, ω f and K and ω h denotes the modulus of continuity of h.

Suppose that h is a harmonic mapping of the unit disc onto a C 1,? domain D. We give sufficient and necessary conditions in terms of boundary function that h is q.c. We announce some new results and also outline application to existence problem of mean distortion minimizers in the Universal Teichm?ller space.

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