Abstract
We show that the visual angle metric and the triangular ratio metric are comparable in convex domains. We also find the extremal points for the visual angle metric in the half space and in the ball by use of a construction based on hyperbolic geometry. Furthermore, we study distortion properties of quasiconformal maps with respect to the triangular ratio metric and the visual angle metric.
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Acknowledgments
The research of the first author was supported by a grant from CIMO. The research of the third author was supported by Academy of Finland project No. 268009. The authors are indebted to Xiaohui Zhang for discussions on Sect. 3, and the referee for valuable suggestions.
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Communicated by Edward Crane.
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Hariri, P., Vuorinen, M. & Wang, G. Some Remarks on the Visual Angle Metric. Comput. Methods Funct. Theory 16, 187–201 (2016). https://doi.org/10.1007/s40315-015-0137-8
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DOI: https://doi.org/10.1007/s40315-015-0137-8