Asymptotic Behaviour of λ-Convex Sets in the Hyperbolic Plane

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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 languageEnglish
Pages (from-to)275-289
JournalGeometriae Dedicata
Volume76
Issue number3
DOIs
Publication statusPublished - 1 Jan 1999

Keywords

  • Hyperbolic plane
  • Integral geometry
  • λ-convex set

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