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The lower bound for the modulus of the derivatives and Jacobian of harmonic injective mappings

Mateljević Miodrag (Faculty of Mathematics, Belgrade)

We give the lower bound for the modulus of the radial derivatives and Jacobian of harmonic injective mappings from the unit ball onto convex domain in plane and space. As an application we show co-Lipschitz property of some classes of qch mappings. We also review related results in planar case using some novelty.

Keywords: Harmonic mappings, Quasi conformal mappings