L'aire des triangles ideaux en geometrie de Hilbert

Details L'aire des triangles ideaux en geometrie de Hilbert L'aire des triangles ideaux en geometrie de Hilbert

2003-12-08

arxiv.org/abs/math/0312163v1

L'enseignement mathematique t. 50 (2004) p. 203-237

Mathematics

Differential Geometry

32 pages, 16 figures

Scientific paper

In this paper we study the area of ideals triangles in a convex domain with its Hilbert geometry. We obtain a characterization of the hyperbolic geometry among all the Hilbert geometry in terms of area of ideals triangles. We also obtain a sharp lower bound on the hilbert area of ideal triangles, independant of the convex, which characterizes the triangle domains in the plane. Furthermore, under specific geometric assumptions, we obtain an upper bound, which depends on the convex domain.

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