Sur la multiplicité des valeurs propres du Laplacien de Witten

Jammes, Pierre

doi:10.1090/S0002-9947-2012-05363-3

Sur la multiplicité des valeurs propres du Laplacien de Witten
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Trans. Amer. Math. Soc. 364 (2012), 2825-2845 Request permission

Abstract:

On any compact manifold of dimension greater than 4, we prescribe the volume and any finite part of the spectrum of the Witten Laplacian acting on $p$-form for $0<p<n$. In particular, we prescribe the multiplicity of the first eigenvalues. On 3-dimensional manifolds, we give examples of a multiple first eigenvalue for 1-forms whose multiplicity depends on the maximal genus of embedded surfaces, all of whose 1-cohomology is induced by the cohomology of the manifold. In particular, this multiplicity is at least 3.

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