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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 of the laplacian acting on p-forms and metric conformal deformations
    (2006)
    Colbois, Bruno 
    ;
    El Soufi, Ahmad
    Let (M, g) be a compact connected orientable Riemannian manifold of dimension n >= 4 and let lambda(k,p)(g) be the k-th positive eigenvalue of the Laplacian. Delta g,p = dd* + d* d acting on differential forms of degree p on M. We prove that the metric g can be conformally deformed to a metric g', having the same volume as g, with arbitrarily large lambda 1, p(g') for all p is an element of [2,n-2]. Note that for the other values of p, that is p = 0, 1, n-1 and n, one can deduce from the literature that, for all k > 0, the k-th eigenvalue lambda(k,p) is uniformly bounded on any conformal class of metrics of fixed volume on M. For p = 1, we show that, for any positive integer N, there exists a metric g(N) conformal to g such that, for all k