JournalszaaVol. 20, No. 1pp. 17–34

A Quaternionic Beltrami-Type Equation and the Existence of Local Homeomorphic Solutions

  • Paula Cerejeiras

    Universidade de Aveiro, Portugal
  • Klaus Gürlebeck

    Bauhaus-Universität Weimar, Germany
  • Uwe Kähler

    Universidade de Aveiro, Portugal
  • H. Malonek

    Universidade de Aveiro, Portugal
A Quaternionic Beltrami-Type Equation and the Existence of Local Homeomorphic Solutions cover
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Abstract

The paper deals with a quaternionic Beltrami-type equation, which is a very natural generalization of the complex Beltrami equation to higher dimensions. Special attention is paid to the systematic use of the embedding of the set of quaternions HintoC2\mathbb H into \mathbb C^2 and the corresponding application of matrix singular integral operators. The proof of the existence of local homeomorphic solutions is based on a necessary and sufficient criterion, which relates the Jacobian determinant of a mapping from R4\mathbb R^4 into R4\mathbb R^4 to the quaternionic derivative of a monogenic function.

Cite this article

Paula Cerejeiras, Klaus Gürlebeck, Uwe Kähler, H. Malonek, A Quaternionic Beltrami-Type Equation and the Existence of Local Homeomorphic Solutions. Z. Anal. Anwend. 20 (2001), no. 1, pp. 17–34

DOI 10.4171/ZAA/1002