Article
| Title: | Möbius metric in sector domains (English) |
| Author: | Rainio, Oona |
| Author: | Vuorinen, Matti |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 73 |
| Issue: | 1 |
| Year: | 2023 |
| Pages: | 213-236 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The Möbius metric $\delta _G$ is studied in the cases, where its domain $G$ is an open sector of the complex plane. We introduce upper and lower bounds for this metric in terms of the hyperbolic metric and the angle of the sector, and then use these results to find bounds for the distortion of the Möbius metric under quasiregular mappings defined in sector domains. Furthermore, we numerically study the Möbius metric and its connection to the hyperbolic metric in polygon domains. (English) |
| Keyword: | hyperbolic geometry |
| Keyword: | hyperbolic metric |
| Keyword: | intrinsic geometry |
| Keyword: | Möbius metric |
| Keyword: | quasiregular mapping |
| Keyword: | triangular ratio metric |
| MSC: | 30C62 |
| MSC: | 51M10 |
| idZBL: | Zbl 07655764 |
| idMR: | MR4541098 |
| DOI: | 10.21136/CMJ.2022.0050-22 |
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| Date available: | 2023-02-03T11:13:11Z |
| Last updated: | 2023-09-13 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/151513 |
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| Reference: | [7] Hariri, P., Vuorinen, M., Zhang, X.: Inequalities and bi-Lipschitz conditions for the triangular ratio metric.Rocky Mt. J. Math. 47 (2017), 1121-1148. Zbl 1376.30019, MR 3689948, 10.1216/RMJ-2017-47-4-1121 |
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| Reference: | [9] Hästö, P., Ibragimov, Z., Minda, D., Ponnusamy, S., Swadesh, S.: Isometries of some hyperbolic-type path metrics, and the hyperbolic medial axis.In the Tradition of Ahlfors-Bers. IV Contemporary Mathematics 432. AMS, Providence (2007), 63-74. Zbl 1147.30029, MR 2342807, 10.1090/conm/432 |
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| Reference: | [12] Rainio, O.: Intrinsic quasi-metrics.Bull. Malays. Math. Sci. Soc. (2) 44 (2021), 2873-2891. Zbl 1476.51019, MR 4296316, 10.1007/s40840-021-01089-9 |
| Reference: | [13] Rainio, O., Vuorinen, M.: Introducing a new intrinsic metric.Result. Math. 77 (2022), Article ID 71, 18 pages. Zbl 07490182, MR 4379104, 10.1007/s00025-021-01592-2 |
| Reference: | [14] Rainio, O., Vuorinen, M.: Triangular ratio metric under quasiconformal mappings in sector domains.To appear in Comput. Methods Funct. Theory (2022). MR 4584499, 10.1007/s40315-022-00447-3 |
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