Landau's theorems for certain biharmonic mappings

Ming-Sheng Liu; Zhi-Wen Liu; Yu-Can Zhu

Landau's theorems for certain biharmonic mappings

Complex Variables 2015-11-17 v1

Authors: Ming-Sheng Liu , Zhi-Wen Liu , Yu-Can Zhu

Abstract

Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$ . In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.

Keywords

harmonic maps harmonic functions mapping theory

Cite

@article{arxiv.1511.04642,
  title  = {Landau's theorems for certain biharmonic mappings},
  author = {Ming-Sheng Liu and Zhi-Wen Liu and Yu-Can Zhu},
  journal= {arXiv preprint arXiv:1511.04642},
  year   = {2015}
}

Comments

12 pages

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