Uniformly locally univalent harmonic mappings |
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Authors: | Saminathan Ponnusamy Jinjing Qiao Xiantao Wang |
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Affiliation: | 1.Department of Mathematics,Indian Institute of Technology Madras,Chennai,India;2.Department of Mathematics,Hebei University,Baoding,People’s Republic of China;3.Department of Mathematics,Shantou University,Shantou,People’s Republic of China |
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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}(lambda )) of uniformly locally univalent harmonic mappings. Finally, we show that the subclass of k-quasiconformal harmonic mappings in ({{mathcal {B}}}_{H}(lambda )) and the class ({{mathcal {B}}}_{H}(lambda )) are contained in the Hardy space of a specific exponent depending on (lambda ), respectively, and we also discuss the growth of coefficients for harmonic mappings in ({{mathcal {B}}}_{H}(lambda )). |
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