The distortion of tetrads under quasimeromorphic mappings of Riemann sphere
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 sp...
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| Format: | Article |
| Language: | English |
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ATNAA
2023-03-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
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| Online Access: | https://atnaea.org/index.php/journal/article/view/35/34 |
| Summary: | 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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| ISSN: | 2587-2648 |