Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm
Complex Variables
2018-01-08 v2
Abstract
In this paper, we consider the class of uniformly locally univalent harmonic mappings in the unit disk and build a relationship between its pre-Schwarzian norm and uniformly hyperbolic radius. Also, we establish eight ways of characterizing uniformly locally univalent sense-preserving harmonic mappings. We also present some sharp distortions and growth estimates and investigate their connections with Hardy spaces. Finally, we study subordination principles of norm estimates.
Keywords
Cite
@article{arxiv.1707.01569,
title = {Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm},
author = {Gang Liu and Saminathan Ponnusamy},
journal= {arXiv preprint arXiv:1707.01569},
year = {2018}
}
Comments
28 pages; The article is to appear in Indagationes Mathematicae