The distortion of tetrads under quasimeromorphic mappings of Riemann sphere

Abstract

On the Riemann sphere, we consider the ptolemaic characteristic of a four of non-empty pairwise non-intersecting compact subsets (generalized tetrad, or generalized angle). We obtain an estimate for distortion of this characteristic under the inverse to a K-quasimeromorphic mapping of the Riemann sphere which takes each of its values at no more then N different points. The distortion function in this estimate depends only on K and N. In the case K=1, it is an essentially new property of complex rational functions.

Keywords

• generalized tetrad
• generalized angle
• ptolemaic characteristic
• value of generalized angle
• quasimeromorphic mapping
• rational function
• quasiconformal mapping