The distortion of tetrads under quasimeromorphic mappings of Riemann sphere

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Advances in the Theory of Nonlinear Analysis and its Application
Volume:7 Issue:1
The distortion of tetrads under quasimeromorphic mappings of Riemann sphere

The distortion of tetrads under quasimeromorphic mappings of Riemann sphere

Pages : 189-194

View : 44 | Download : 103

Publication Date : 2023-03-31

Article Type : Research Paper

Abstract :On the Riemann sphere, we consider the ptolemaic characteristic of a four of non-empty pairwise non-intersecting compact subsets insert ignore into journalissuearticles values(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

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