Uniformly locally univalent harmonic mappings

2016/01/06 by Saminathan Ponnusamy, Ponnusamy, S., Jing Qiao +3
Mathematics · #30C45 #30C50 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 30C65 #Secondary: 30C20

paper · pdf · doi:10.48550/arxiv.1601.01139

openalex publication_date 2016/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The primary aim of this paper is to characterize the uniformly locally univalent harmonic mappings in the unit disk. Then, we obtain sharp distortion, growth and covering theorems for one parameter family \mathcal B_H(λ) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of k-quasiconformal harmonic mappings in \mathcal B_H(λ) and the class \mathcal B_H(λ) are contained in the Hardy space of a specific exponent depending on the λ, respectively, and we also discuss the growth of coefficients for harmonic mappings in \mathcal B_H(λ).

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