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Quaternionic Beltrami-type equations and homeomorphic solutions

Abstract

In this paper we deal with a special type of quaternionic Beltrami equation and discuss the existence of local and global homeomorphic solutions based on a necessary and sufficient condition, which relates the Jacobian determinant of a mapping from ℝ4 to ℝ4 with the hypercomplex derivative of a monogenic function.

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Dedicated to Loo-Keng Hua on the occasion of his 90th birthday

This paper was done while the first author was a recipient of a PRAXIS XXI-scholarship of the Fundação para a Ciência e a Tecnologia visiting the Universidade de Aveiro in Portugal.

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Kähler, U., Martins, A.M. Quaternionic Beltrami-type equations and homeomorphic solutions. AACA 11, 177–182 (2001). https://doi.org/10.1007/BF03219130

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Keywords

  • Beltrami equations
  • quaternionic analysis
  • hypercomplex derivative
  • quasiconformal mappings

MSC 2000

  • 30G35
  • 30G20