Möbius metric in sector domains

Oona Rainio; Matti Vuorinen

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 1, page 213-236
  • ISSN: 0011-4642

Abstract

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The Möbius metric δ 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.

How to cite

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Rainio, Oona, and Vuorinen, Matti. "Möbius metric in sector domains." Czechoslovak Mathematical Journal 73.1 (2023): 213-236. <http://eudml.org/doc/299508>.

@article{Rainio2023,
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.},
author = {Rainio, Oona, Vuorinen, Matti},
journal = {Czechoslovak Mathematical Journal},
keywords = {hyperbolic geometry; hyperbolic metric; intrinsic geometry; Möbius metric; quasiregular mapping; triangular ratio metric},
language = {eng},
number = {1},
pages = {213-236},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Möbius metric in sector domains},
url = {http://eudml.org/doc/299508},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Rainio, Oona
AU - Vuorinen, Matti
TI - Möbius metric in sector domains
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 1
SP - 213
EP - 236
AB - 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.
LA - eng
KW - hyperbolic geometry; hyperbolic metric; intrinsic geometry; Möbius metric; quasiregular mapping; triangular ratio metric
UR - http://eudml.org/doc/299508
ER -

References

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  6. Hariri, P., Klén, R., Vuorinen, M., 10.1007/978-3-030-32068-3, Springer Monographs in Mathematics. Springer, Cham (2020). (2020) Zbl1450.30003MR4179585DOI10.1007/978-3-030-32068-3
  7. Hariri, P., Vuorinen, M., Zhang, X., 10.1216/RMJ-2017-47-4-1121, Rocky Mt. J. Math. 47 (2017), 1121-1148. (2017) Zbl1376.30019MR3689948DOI10.1216/RMJ-2017-47-4-1121
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  11. Nasser, M. M. S., Rainio, O., Vuorinen, M., 10.1016/j.camwa.2021.11.016, Comput. Math. Appl. 105 (2022), 54-74. (2022) Zbl07447596MR4345260DOI10.1016/j.camwa.2021.11.016
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