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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.