The distortion of tetrads under quasimeromorphic mappings of Riemann sphere

Year 2023, Volume: 7 Issue: 1, 189 - 194, 31.03.2023

Vladislav Aseev

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

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