Abstract:
We consider the Ptolemaic characteristic of quadruples of disjoint nonempty compact subsets (generalized tetrads). The main theorem of this article asserts that an arbitrary multivalued mapping $F$ from ${\Bbb R}^n$ onto itself such that the images of distinct points are disjoint and each of them contains at most two distinct points is the inverse of a $K$-quasimeromorphic mapping if and only if $F$ admits a controllable upper bound for the distortion of the Ptolemaic characteristic of tetrads.
Keywords:mapping with bounded distortion, quasiregular mapping, quasimeromorphic mapping, quasimöbius mapping, multivalued mapping, Ptolemaic characteristic of tetrads.
Fulltext:
PDF file (272 kB)