Pluriharmonic mappings and linearly connected domains in ℂ n

Martin Chuaqui; Hidetaka Hamada; Rodrigo Hernández; Gabriela Kohr

doi:10.1007/s11856-014-0027-1

Pluriharmonic mappings and linearly connected domains in ℂⁿ

Martin Chuaqui, Hidetaka Hamada, Rodrigo Hernández, Gabriela Kohr

Faculty of Engineering and Science

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball Bⁿ 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 Bⁿ into ℂⁿ.

Original language	English
Pages (from-to)	489-506
Number of pages	18
Journal	Israel Journal of Mathematics
Volume	200
Issue number	1
DOIs	https://doi.org/10.1007/s11856-014-0027-1
State	Published - 18 Jun 2014

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title = "Pluriharmonic mappings and linearly connected domains in ℂ n",

abstract = "In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball Bn of ℂn. The results are generalizations of conditions of Chuaqui and Hern{\'a}ndez 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 Hern{\'a}ndez and Mart{\'i}n on a shear type construction for planar harmonic mappings, by adapting the concept of stable univalence to pluriharmonic mappings of the unit ball Bn into ℂn.",

author = "Martin Chuaqui and Hidetaka Hamada and Rodrigo Hern{\'a}ndez and Gabriela Kohr",

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AU - Chuaqui, Martin

AU - Hamada, Hidetaka

AU - Hernández, Rodrigo

AU - Kohr, Gabriela

PY - 2014/6/18

Y1 - 2014/6/18

N2 - In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball Bn 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 Bn into ℂn.

AB - In this paper we obtain certain sufficient conditions for the univalence of pluriharmonic mappings defined in the unit ball Bn 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 Bn into ℂn.

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SP - 489

EP - 506

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Pluriharmonic mappings and linearly connected domains in ℂ n

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Pluriharmonic mappings and linearly connected domains in ℂⁿ