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Extreme points of subordination and weak subordination families of harmonic mappings

Jinjing Qiao; Xiantao Wang — 2011

Czechoslovak Mathematical Journal

The aim of the paper is to discuss the extreme points of subordination and weak subordination families of harmonic mappings. Several necessary conditions and sufficient conditions for harmonic mappings to be extreme points of the corresponding families are established.

A characterization of Fuchsian groups acting on complex hyperbolic spaces

Xi Fu; Liulan Li; Xiantao Wang — 2012

Czechoslovak Mathematical Journal

Let $G \subset 𝐒𝐔 (2, 1)$ be a non-elementary complex hyperbolic Kleinian group. If $G$ preserves a complex line, then $G$ is $ℂ$ -Fuchsian; if $G$ preserves a Lagrangian plane, then $G$ is $ℝ$ -Fuchsian; $G$ is Fuchsian if $G$ is either $ℂ$ -Fuchsian or $ℝ$ -Fuchsian. In this paper, we prove that if the traces of all elements in $G$ are real, then $G$ is Fuchsian. This is an analogous result of Theorem V.G. 18 of B. Maskit, Kleinian Groups, Springer-Verlag, Berlin, 1988, in the setting of complex hyperbolic isometric groups. As an application...

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