Geodesic
Möbius metric in sector domains
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 213-236
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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.
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.
DOI : 10.21136/CMJ.2022.0050-22
Classification : 30C62, 51M10
Keywords: hyperbolic geometry; hyperbolic metric; intrinsic geometry; Möbius metric; quasiregular mapping; triangular ratio metric 
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Rainio, Oona; Vuorinen, Matti. Möbius metric in sector domains. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 213-236. doi: 10.21136/CMJ.2022.0050-22

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