The analogue of Picard's theorem for quasiregular mappings in dimension three

Abstract

The theory of quasiregular mappings has turned out to be the fight extension of the geometric parts of the theory of analytic functions in the plane to real n-dimensional space. The study of these mappings was initiated by Re~etnjak around 1966 and his main contributions to the theory is presented in the recent book [8]. For the basic theory of quasiregular mappings we refer to [2], [3], [13]. The definition is given in Section 2.1. In 1967 Zofi~ [14] raised the question of the validity o f a Picard's theorem on omitted values for quasiregular mappings. Such a theorem appeared in 1980 in the following form.