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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
    Eigenvalue pinching on convex domains in space forms
    (2009)
    Aubry, Erwann
    ;
    Bertrand, Jérôme
    ;
    Colbois, Bruno 
    In this paper, we show that the convex domains of H-n which are almost extremal for the Faber-Krahn or the Payne-Polya-Weinberger inequalities are close to geodesic balls. Our proof is also valid in other space forms and allows us to recover known results in R-n and S-n.
  • Publication
    Métadonnées seulement
    Capacité et inégalité de Faber-Krahn dans Rn
    (2006-4-18)
    Bertrand, Jérôme
    ;
    Colbois, Bruno 
    In this paper, we define a new capacity which allows us to control the behaviour of the Dirichlet spectrum of a compact Riemannian manifold with boundary, with "small" subsets (which may intersect the boundary) removed. This result generalises a classical result of Rauch and Taylor ("the crushed ice theorem"). In the second part, we show that the Dirichlet spectrum of a sequence of bounded Euclidean domains converges to the spectrum of a ball with the same volume, if the first eigenvalue of these domains converges to the first eigenvalue of a ball.