Some remarks on the visual angle metric. (English) Zbl 1355.30019
The local behavior of quasiconformal mappings in terms of different metrics in Euclidean space is studied. The so-called hyperbolic metric and distance ratio metric are introduced. The relationship between the two metrics mentioned above is obtained. In the case of the half-space and the ball, the extremal points for the visual angle metric are found. Uniform continuity of quasiconformal maps with respect to the triangular ratio metric and the visual angle metric is obtained.
Reviewer: Evgeny Sevost’yanov (Donetsk)
MSC:
| 30C65 | Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations |
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