Abstract
It is known that the limit Area/Length for a sequence of convex sets expanding over the whole hyperbolic plane is less than or equal 1, and exactly 1 when the sets considered are convex with respect to horocycles. We consider geodesics and horocycles as particular cases of curves of constant geodesic curvature λ with 0 ≥ λ ≤ 1 and we study the above limit Area/Length as a function of the parameter λ.
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Gallego, E., Reventós, A. Asymptotic Behaviour of λ-Convex Sets in the Hyperbolic Plane. Geometriae Dedicata 76, 275–289 (1999). https://doi.org/10.1023/A:1005130211872
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DOI: https://doi.org/10.1023/A:1005130211872