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Landau–Bloch type theorems for strongly bounded harmonic mappings

  • Ming-Sheng LiuEmail author
  • Li-Fang Luo
  • Xi Luo
Article
  • 13 Downloads

Abstract

In this paper, we first establish the sharp version of Landau–Bloch type theorem for strongly bounded harmonic mappings by considering the Landau–Bloch type theorem of a one-parameter family of holomorphic mappings. Next, we will establish two sharp versions of Landau–Bloch type theorems for certain harmonic mappings. Finally, we also pose several conjectures for the sharp version of Landau–Bloch type theorem for bounded harmonic mappings.

Keywords

Landau–Bloch type theorem Landau theorem Bloch theorem Planar harmonic mapping Univalent 

Mathematics Subject Classification

Primary 30C99 Secondary 30C62 

Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesSouth China Normal UniversityGuangzhouPeople’s Republic of China
  2. 2.School of MathematicsJiaying UniversityMeizhouChina

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