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Partial differential equations connected with some Clifford structures and the related quasiconformal mappings. (English) Zbl 0668.30038

A concept of a Hurwitz pair and the corresonding supercomplex structures is now considered in a slightly more general setting of a weighted Hurwitz pair, thus giving a further development of recent papers by the authors on complex geometrical aspects of Clifford algebras. The framework seems impotant when investigating certain partial differential equations of mathematical physics which we call Hurwitz equation with mass. This throws some light on the generalized Dirac equations and soliton equations of Kadomtsev-Petviashvili type. In a particular case we arrive at an elegant description of quasiconformal mappings in the plane, in which an important role is played by the method of isospectral deformations. This paper is in final form and no version of it will be submitted for publication elsewhere.

MSC:

30G35 Functions of hypercomplex variables and generalized variables
30C62 Quasiconformal mappings in the complex plane
35Jxx Elliptic equations and elliptic systems
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