Les géométries de Hilbert sont à géométrie locale bornée

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dc.creatorColbois, Bruno
dc.creatorVernicos, Constantin
dc.date2006-04-21
dc.date.accessioned2026-07-07T08:23:49Z
dc.date.available2026-07-07T08:23:49Z
dc.descriptionWe prove that the Hilbert geometry of a convex domain in ${\mathbb R}^n$ has bounded local geometry, i.e., for a given radius, all balls are bilipschitz to a euclidean domain of ${\mathbb R}^n$. As a consequence, if the Hilbert geometry is also Gromov hyperbolic, then the bottom of its spectrum is strictly positive. We also give a counter exemple in dimension three which shows that the reciprocal is not true for non plane Hilbert geometries.
dc.descriptionA paraître aux annales de l'Institut Fourier
dc.identifierhttps://arxiv.org/abs/math/0604461
dc.identifierhttp://arxiv.org/abs/math/0604461
dc.identifierAnnales de l'Institut Fourier 57, 4 (2007) 1359-1375
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/136135
dc.subjectDifferential Geometry
dc.subjectMetric Geometry
dc.titleLes géométries de Hilbert sont à géométrie locale bornée
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