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).
Keywords:mapping with bounded distortion, quasiregular mapping, quasimeromorphic mapping, graphical convergence, graphical limit, Ptolemaic characteristic of a tetrad, quasimöbius property.
Fulltext:
PDF file (310 kB)