Generalized Angles in Ptolemaic Möbius Structures

Аннотация

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: X → 2Y 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 ℝ̅ⁿ lies in this class.