Inclusion properties of the triangular ratio metric balls. (English) Zbl 07797003
Summary: Inclusion properties are studied for balls of the triangular ratio metric, the hyperbolic metric, the \(j^\ast\)-metric, and the distance ratio metric defined in the unit ball domain. Several sharp results are proven and a conjecture about the relation between triangular ratio metric balls and hyperbolic balls is given. An algorithm is also built for drawing triangular ratio circles or three-dimensional spheres.
MSC:
| 51M10 | Hyperbolic and elliptic geometries (general) and generalizations |
| 51M16 | Inequalities and extremum problems in real or complex geometry |
Keywords:
distance ratio metric; hyperbolic geometry; hyperbolic metric; metric balls; triangular ratio metricReferences:
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