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Linear connectivity, Schwarz–Pick lemma and univalency criteria for planar harmonic mapping

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, 421008, P. R. China

    Shao Lin Chen

  2. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600 113, India

    Saminathan Ponnusamy

  3. Department of Mathematics and Systems Analysis, Aalto University, P. O. Box 11100, FI-00076, Aalto, Finland

    Antti Rasila

  4. Department of Mathematics, Shantou University, Shantou, 515063, P. R. China

    Xian Tao Wang

Authors
  1. Shao Lin Chen
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  2. Saminathan Ponnusamy
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  3. Antti Rasila
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  4. Xian Tao Wang
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Corresponding author

Correspondence to Xian Tao Wang.

Additional information

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

This author is on leave from the Indian Institute of Technology Madras

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Chen, S.L., Ponnusamy, S., Rasila, A. et al. Linear connectivity, Schwarz–Pick lemma and univalency criteria for planar harmonic mapping. Acta. Math. Sin.-English Ser. 32, 297–308 (2016). https://doi.org/10.1007/s10114-016-4259-3

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  • DOI: https://doi.org/10.1007/s10114-016-4259-3

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