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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
    Métadonnées seulement
    Eigenvalues estimate for the Neumann problem of a bounded domain
    (2008-12-21)
    Colbois, Bruno 
    ;
    Maerten, Daniel
    In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Omega in a given complete ( not compact a priori) Riemannian manifold ( M, g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As applications, we prove that if the Ricci curvature of ( M, g) is bounded below Ric(g) >= -( n - 1) a(2), a >= 0, then there exist constants A(n) > 0, B-n > 0 only depending on the dimension, such that lambda(k)(Omega)
  • 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.