| Linear Connectivity,Schwarz–Pick Lemma and Univalency Criteria for Planar Harmonic Mapping |
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| 基金项目： | Supported by National Natural Science Foundation of China (Grant Nos. 11401184 and 11571216), Hu'nan Province Natural Science Foundation of China (Grant No. 2015JJ3025), the Excellent Doctoral Dissertation of Special Foundation of Hu'nan Province (higher education 2050205), the Construct Program of the Key Discipline in Hu'nan Province (Grant No. [2011]76), Academy of Finland (Grant No. 278328), and the Väisälä Foundation of the Finnish Academy of Science and Letters |
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| 摘 要： | 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.
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