Graphical Limits of Quasimeromorphic Mappings and Distortion of the Characteristic of Tetrads

Abstract

We fully describe the form of the graphical limit of a sequence of \( K \)-quasimeromorphic mappings of a domain \( D \) in \( \overline{R^{n}} \) which take each of its values at \( N \) distinct points at most. For the family of all \( K \)-quasimeromorphic mappings of \( \overline{R^{n}} \) onto itself taking each value at \( N \) points at most we establish the presence of a common estimate for the distortion of the Ptolemaic characteristic of generalized tetrads (quadruples of disjoint compact sets).