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Journal Articles Annales de l'Institut Fourier Year : 2014

Finitude géométrique en géométrie de Hilbert

Abstract

We study the notion of geometrical finiteness for those Hilbert geometries defined by strictly convex sets with $\mathcal{C}^1$ boundary. In Gromov-hyperbolic spaces, geometrical finiteness is defined by a property of the group action on the boundary of the space. We show by constructing an explicit counter-example that this definition has to be strenghtened in order to get equivalent characterizations in terms of the geometry of the quotient orbifold, similar to those obtained by Brian Bowditch in hyperbolic geometry.
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Dates and versions

hal-00673118 , version 1 (22-02-2012)
hal-00673118 , version 2 (24-02-2012)
hal-00673118 , version 3 (02-10-2013)

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Mickaël Crampon, Ludovic Marquis. Finitude géométrique en géométrie de Hilbert. Annales de l'Institut Fourier, 2014, 64 (6), pp.2299-2377. ⟨10.5802/aif.2914⟩. ⟨hal-00673118v3⟩
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