Hilbert geometry for convex polygonal domains

Bruno Colbois (1) , Constantin Vernicos (2) , Patrick Verovic (3)

1 UNINE - Institut de Mathématiques
2 I3M - Institut de Mathématiques et de Modélisation de Montpellier
3 LAMA - Laboratoire de Mathématiques

We prove in this paper that the Hilbert geometry associated with an open convex polygonal set is Lipschitz equivalent to Euclidean plane.

Domaines: Géométrie métrique [math.MG]

Bruno Colbois, Constantin Vernicos, Patrick Verovic. Hilbert geometry for convex polygonal domains. Journal of Geometry, 2011, 100, pp.37-64. ⟨10.1007/s00022-011-0066-2⟩. ⟨hal-00271373⟩