2015/10/16 by Graf, Sergey Yu., Ponnusamy, Saminathan, Starkov, Victor V.
#30C75 #31A05 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 30C62 #Secondary: 30C45
paper · doi:10.48550/arxiv.1510.04886
In this paper, we obtain a new characterization for univalent harmonic mappings and obtain a structural formula for the associated function which defines the analytic Φ-like functions in the unit disk. The new criterion stated in this article for the injectivity of harmonic mappings implies the well-known results of Kas'yanyuk \citeKas59 and Brickman \citeBrick73 for analytic functions, but with a simpler proof than theirs. A number of consequences of the characterization, and examples are also presented. Further investigation provides a new method to construct univalent harmonic mappings with the help of an improved distortion theorem.