The Landau-Bloch type theorems for planar harmonic mappings with bounded dilation

[摘要] In this paper, we first establish the sharp version of Landau-Bloch type theorem for holomorphic functions with bounded derivative by applying Schwarz-Pick lemma. Next, we derive the sharp version of Landau-Bloch type theorem for planar harmonic mappings with bounded dilation by applying geometric method. Furthermore, all extremal functions are also provided under suitable restriction. (C) 2018 Elsevier Inc. All rights reserved.

[发布日期] 2018-12-15

[关键词] Harmonic mappings;Univalent;Landau-Bloch type theorem;The extremal function