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 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 into to the quaternionic derivative of a monogenic function.
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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. 17–34DOI 10.4171/ZAA/1002