Abstract
AbstractThe hyperbolic metric and different hyperbolic type metrics are studied in open sector domains of the complex plane. Several sharp inequalities are proven for them. Our main result describes the behavior of the triangular ratio metric under quasiconformal maps from one sector onto another one.
Funder
University of Turku (UTU) including Turku University Central Hospital
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Theory and Mathematics,Analysis
Reference19 articles.
1. Aksoy, A.G., Ibragimov, Z., Whiting, W.: Averaging one-point hyperbolic-type metrics. Proc. Am. Math. Soc. 146(12), 5205–5218 (2018)
2. Beardon, A.F., Minda, D.: The hyperbolic metric and geometric function theory. In: Ponnusamy, S., Sugawa, T., Vuorinen, M. (eds.) Proceedings of International Workshop on Quasiconformal Mappings and their Applications (IWQCMA05), pp. 9–56 (2006)
3. Buckley, S., Herron, D.: Quasihyperbolic geodesics are hyperbolic quasi-geodesics. J. Eur. Math. Soc. 22(6), 1917–1970 (2020)
4. Chen, J., Hariri, P., Klén, R., Vuorinen, M.: Lipschitz conditions, triangular ratio metric, and quasiconformal maps. Ann. Acad. Sci. Fenn. Math. 40, 683–709 (2015)
5. Fujimura, M., Mocanu, M., Vuorinen, M.: Barrlund’s distance function and quasiconformal maps. Complex Var. Elliptic Equ. 66(8), 1225–1255 (2021)
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