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Colbois, Bruno

Nom
Colbois, Bruno
Affiliation principale
Site web
Fonction
Professeur ordinaire
Email
Bruno.Colbois@unine.ch
Identifiants
https://libra.unine.ch/handle/123456789/456
_
0000-0002-8514-4315

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  • Publication
    Accès libre
    Two properties of volume growth entropy in Hilbert geometry
    (2014-11-9)
    Colbois, Bruno 
    ;
    Verovic, Patrick
    The aim of this paper is to provide two examples in Hilbert geometry which show that volume growth entropy is not always a limit on the one hand, and that it may vanish for a non-polygonal domain in the plane on the other hand.
  • Publication
    Accès libre
    Laplacian and spectral gap in regular Hilbert geometries
    (2014-9-19)
    Barthelmé, Thomas
    ;
    Colbois, Bruno 
    ;
    Crampon, Mickael
    ;
    Verovic, Patrick
    We study the spectrum of the Finsler--Laplace operator for regular Hilbert geometries, defined by convex sets with C2 boundaries. We show that for an n-dimensional geometry, the spectral gap is bounded above by (n−1)2/4, which we prove to be the infimum of the essential spectrum. We also construct examples of convex sets with arbitrarily small eigenvalues.
  • Publication
    Métadonnées seulement
  • Publication
    Métadonnées seulement
    Hilbert geometry for convex polygonal domains
    (2011-1-21)
    Colbois, Bruno 
    ;
    Vernicos, Constantin
    ;
    Verovic, Patrick
  • Publication
    Métadonnées seulement
    Some smooth Finsler deformations of hyperbolic surfaces
    (2009)
    Colbois, Bruno 
    ;
    Newberger, Florence
    ;
    Verovic, Patrick
    Given a closed hyperbolic Riemannian surface, the aim of the present paper is to describe an explicit construction of smooth deformations of the hyperbolic metric into Finsler metrics that are not Riemannian and whose properties are such that the classical Riemannian results about entropy rigidity, marked length spectrum rigidity and boundary rigidity all fail to extend to the Finsler category.
  • Publication
    Métadonnées seulement
    Area of ideal triangles and Gromov hyperbolicity in Hilbert Geometry
    (2008)
    Colbois, Bruno 
    ;
    Vernicos, Constantin
    ;
    Verovic, Patrick
  • Publication
    Métadonnées seulement
    L'aire des triangles idéaux en géométrie de Hilbert
    (2004-12-20)
    Colbois, Bruno 
    ;
    Vernicos, Constantin
    ;
    Verovic, Patrick
  • Publication
    Métadonnées seulement
    Hilbert geometry for strictly convex domains
    (2004)
    Colbois, Bruno 
    ;
    Verovic, Patrick
    We prove in this paper that the Hilbert geometry associated with a bounded open convex domain C in R-n whose boundary partial derivativeC is a C-2 hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H-n. Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H-n.
  • Publication
    Métadonnées seulement
    Rigidity of Hilbert metrics
    (2002)
    Colbois, Bruno 
    ;
    Verovic, Patrick
    We study the groups of isometries for Hilbert metrics on bounded open convex domains in R-n and show that if C is such a set with a strictly convex boundary, the Hilbert geometry is asymptotically Riemannian at infinity. As a consequence of this result, we prove there are no Hausdorff quotients of C by isometry subgroups with finite volume except when partial derivativeC is an ellipsoid.