Israel Journal of Mathematics

, Volume 200, Issue 1, pp 489–506 | Cite as

Pluriharmonic mappings and linearly connected domains in ℂn

  • Martin Chuaqui
  • Hidetaka Hamada
  • Rodrigo Hernández
  • Gabriela Kohr
Article

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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Copyright information

© Hebrew University of Jerusalem 2014

Authors and Affiliations

  • Martin Chuaqui
    • 1
  • Hidetaka Hamada
    • 2
  • Rodrigo Hernández
    • 3
  • Gabriela Kohr
    • 4
  1. 1.Facultad de MatemáticasP. Universidad Católica de ChileCasilla 306, Santiago 22Chile
  2. 2.Faculty of EngineeringKyushu Sangyo UniversityFukuokaJapan
  3. 3.Facultad de Ciencias y TecnologíaUniversidad Adolfo IbáñezViña del MarChile
  4. 4.Faculty of Mathematics and Computer ScienceBabeş-Bolyai UniversityCluj-NapocaRomania

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