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 to 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.
Original language | English |
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Pages (from-to) | 275-289 |
Journal | Geometriae Dedicata |
Volume | 76 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Jan 1999 |
Keywords
- Hyperbolic plane
- Integral geometry
- λ-convex set