- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 7 Issue: 1
- The distortion of tetrads under quasimeromorphic mappings of Riemann sphere
The distortion of tetrads under quasimeromorphic mappings of Riemann sphere
Authors : Vladislav ASEEV
Pages : 189-194
Doi:10.31197/atnaa.1249278
View : 32 | Download : 92
Publication Date : 2023-03-31
Article Type : Research Article
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