Chen, Shao Lin et al., Linear connectivity, Schwarz.Pick lemma and univalency criteria for planar harmonic mapping, Acta mathematica Sinica. English series (Print) , 32(3), 2016, pp. 297-308
In this paper, we first establish a Schwarz.Pick lemma for higher-order derivatives of planar harmonic mappings, and apply it to obtain univalency criteria. Then we discuss distortion theorems, Lipschitz continuity and univalency of planar harmonic mappings defined in the unit disk with linearly connected images.