Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 213-236, 2023

Möbius metric in sector domains

Oona Rainio, Matti Vuorinen

Received February 7, 2022. Published online September 29, 2022. OPEN ACCESS

Abstract: 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.

Keywords: hyperbolic geometry; hyperbolic metric; intrinsic geometry; Möbius metric; quasiregular mapping; triangular ratio metric

Classification MSC: 51M10, 30C62

DOI: 10.21136/CMJ.2022.0050-22

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Oona Rainio (corresponding author), Matti Vuorinen, Department of Mathematics and Statistics, University of Turku, Turun yliopisto, FI-20014 Turku, Finland, e-mail: ormrai@utu.fi, vuorinen@utu.fi

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