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Pluriharmonic mappings and linearly connected domains in ℂn

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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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Authors and Affiliations

  1. Facultad de Matemáticas, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

    Martin Chuaqui

  2. Faculty of Engineering, Kyushu Sangyo University, 3-1 Matsukadai 2-Chome, Higashi-ku, Fukuoka, 813-8503, Japan

    Hidetaka Hamada

  3. Facultad de Ciencias y Tecnología, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile

    Rodrigo Hernández

  4. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 1 M. Kogălniceanu Str, 400084, Cluj-Napoca, Romania

    Gabriela Kohr

Authors
  1. Martin Chuaqui
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  2. Hidetaka Hamada
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  3. Rodrigo Hernández
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  4. Gabriela Kohr
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Corresponding author

Correspondence to Martin Chuaqui.

Additional information

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

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