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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
    Curvature, Harnack's inequality, and a spectral characterization of nilmanifolds
    (2003)
    Aubry, Erwann
    ;
    Colbois, Bruno 
    ;
    Ghanaat, Patrick
    ;
    Ruh, Ernst
    For closed n-dimensional Riemannian manifolds M with almost nonnegative Ricci curvature, the Laplacian on one-forms is known to admit at most n small eigenvalues. If there are n small eigenvalues, or if M is orientable and has n - 1 small eigenvalues, then M is diffeomorphic to a nilmanifold, and the metric is almost left invariant. We show that our results are optimal for n greater than or equal to 4.