Abstract
The Möbius metric δG 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.
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Oona Rainio’s research was funded by the University of Turku Graduate School UTUGS. Open access funding provided by University of Turku.
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Rainio, O., Vuorinen, M. Möbius metric in sector domains. Czech Math J 73, 213–236 (2023). https://doi.org/10.21136/CMJ.2022.0050-22
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DOI: https://doi.org/10.21136/CMJ.2022.0050-22
Keywords
- hyperbolic geometry
- hyperbolic metric
- intrinsic geometry
- Möbius metric
- quasiregular mapping
- triangular ratio metric
MSC 2020
- 51M10
- 30C62