The distortion of tetrads under quasimeromorphic mappings of Riemann sphere
Keywords:
generalized tetrad, generalized angle, ptolemaic characteristic, value of generalized angle, quasimeromorphic mapping, rational function, quasiconformal mappingAbstract
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.
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