Harmonic mappings and finite valency of analytic functions

Abstract

The harmonic mappings of a circle into domains that can be cut into a finite number of convex subdomains has been studied. An estimate of the valency of holomorphic mappings of a circle composed of analytical components of the harmonic function has been obtained. In addition, the Keobe harmonic univalent function has been considered to illustrate the results of the research.

Keywords

• harmonic function
• univalent function
• n-valent function
• convex function
• shear construction