Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mappings

摘要

In this paper, we first establish the Schwarz-Pick lemma of higher-order andapply it to obtain a univalency criteria for planar harmonic mappings. Then wediscuss distortion theorems, Lipschitz continuity and univalency of planarharmonic mappings defined in the unit disk with linearly connected images.