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 |
| Subjects: | |
| Online Access: | https://atnaea.org/index.php/journal/article/view/35/34 |
| _version_ | 1797248524681740288 |
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| author | Vladislav ASEEV |
| author_facet | Vladislav ASEEV |
| author_sort | Vladislav ASEEV |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-24T20:15:58Z |
| format | Article |
| id | doaj.art-129bc3e4bd8045f6aa8db70c97811568 |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-24T20:15:58Z |
| publishDate | 2023-03-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-129bc3e4bd8045f6aa8db70c978115682024-03-22T17:39:34ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482023-03-017118919410.31197/atnaa.1249278The distortion of tetrads under quasimeromorphic mappings of Riemann sphereVladislav ASEEV0Sobolev Institute of Mathematics, RussiaOn 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.https://atnaea.org/index.php/journal/article/view/35/34generalized tetradgeneralized angleptolemaic characteristicvalue of generalized anglequasimeromorphic mappingrational functionquasiconformal mapping |
| spellingShingle | Vladislav ASEEV The distortion of tetrads under quasimeromorphic mappings of Riemann sphere Advances in the Theory of Nonlinear Analysis and its Applications generalized tetrad generalized angle ptolemaic characteristic value of generalized angle quasimeromorphic mapping rational function quasiconformal mapping |
| title | The distortion of tetrads under quasimeromorphic mappings of Riemann sphere |
| title_full | The distortion of tetrads under quasimeromorphic mappings of Riemann sphere |
| title_fullStr | The distortion of tetrads under quasimeromorphic mappings of Riemann sphere |
| title_full_unstemmed | The distortion of tetrads under quasimeromorphic mappings of Riemann sphere |
| title_short | The distortion of tetrads under quasimeromorphic mappings of Riemann sphere |
| title_sort | distortion of tetrads under quasimeromorphic mappings of riemann sphere |
| topic | generalized tetrad generalized angle ptolemaic characteristic value of generalized angle quasimeromorphic mapping rational function quasiconformal mapping |
| url | https://atnaea.org/index.php/journal/article/view/35/34 |
| work_keys_str_mv | AT vladislavaseev thedistortionoftetradsunderquasimeromorphicmappingsofriemannsphere AT vladislavaseev distortionoftetradsunderquasimeromorphicmappingsofriemannsphere |