Abstract
In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball \(\mathbb{B}^n \) of ℂn. The results are generalizations of conditions of Chuaqui and Hernández that relate the univalence of planar harmonic mappings with linearly connected domains, and show how such domains can play a role in questions regarding injectivity in higher dimensions. In addition, we extend recent work of Hernández and Martín on a shear type construction for planar harmonic mappings, by adapting the concept of stable univalence to pluriharmonic mappings of the unit ball \(\mathbb{B}^n \) into ℂn.
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M. Chuaqui and R. Hernández were partially supported by Fondecyt Grants #1110321 and #1110160 (Chile).
H. Hamada was partially supported by JSPS KAKENHI Grant Number 22540213.
G. Kohr was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0899.
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Chuaqui, M., Hamada, H., Hernández, R. et al. Pluriharmonic mappings and linearly connected domains in ℂn . Isr. J. Math. 200, 489–506 (2014). https://doi.org/10.1007/s11856-014-0027-1
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DOI: https://doi.org/10.1007/s11856-014-0027-1