Linear connectivity, Schwarz-Pick lemma and univalency criteria for planar harmonic mapping. (English) Zbl 1336.31003
Summary: 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.
MSC:
| 31A05 | Harmonic, subharmonic, superharmonic functions in two dimensions |
| 30C55 | General theory of univalent and multivalent functions of one complex variable |
References:
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