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arXiv · 1707.01569

Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm

Gang Liu·Saminathan Ponnusamy
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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.

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Gang Liu, Saminathan Ponnusamy. 2017-07-05. Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm. https://arxiv.org/abs/1707.01569

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