Abstract:
We show that each Ptolemaic semimetric is Möbius-equivalent to a bounded metric. Introducing generalized angles in Ptolemaic Möbius structures, we study the class of multivalued mappings $F\colon X\to2^Y$ with a lower bound on the distortion of generalized angles. We prove that the inverse mapping to the coordinate function of a quasimeromorphic automorphism of $\overline{\mathbb R}^n$ lies in this class.
Fulltext:
PDF file (357 kB)
