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

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• 作者：Shao Lin Chen ; Saminathan Ponnusamy…
• 关键词：Harmonic mapping ; linearly connected domain ; Schwarz–Pick lemma ; a ; close ; to ; convex function ; John constant ; univalency ; 30C55 ; 31A05 ; 30C62
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：32
• 期：3
• 页码：297-308
• 全文大小：246 KB
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• 作者单位：Shao Lin Chen (1)
  Saminathan Ponnusamy (2)
  Antti Rasila (3)
  Xian Tao Wang (4)
  
  1. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, 421008, P. R. China
  2. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600 113, India
  3. Department of Mathematics and Systems Analysis, Aalto University, P. O. Box 11100, FI-00076, Aalto, Finland
  4. Department of Mathematics, Shantou University, Shantou, 515063, P. R. China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

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. Keywords Harmonic mapping linearly connected domain Schwarz–Pick lemma a-close-to-convex function John constant univalency