Volume 34 • Number 2 • 2011   • Coefficient Estimates and Landau-Bloch's Constant for Planar Harmonic Mappings Sh. Chen, S. Ponnusamy and X. Wang Abstract. The aim of this paper is to study the properties of planar harmonic mappings. The main results are as follows. First, by using the subordination of analytic functions, a sharp coefficient estimate is obtained and several applications are given. Then two results about Landau-Bloch's constant are proved: one for planar harmonic mappings and the other for \(L(f)\), where \(L\) represents the linear complex operator \(L=z\frac{\partial}{\partial z} -\overline{z}\frac{\partial}{\partial \overline{z}}\) defined on the class of complex-valued \(C^1\) functions in the plane and \(f\) is an open harmonic mapping. 2010 Mathematics Subject Classification: Primary: 30C65, 30C45; Secondary: 30C20. Full text: PDF