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arXiv · 1003.5391

Sur la multiplicité des valeurs propres du laplacien de Witten

Pierre Jammes
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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 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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Pierre Jammes. 2012-04-24. Sur la multiplicité des valeurs propres du laplacien de Witten. https://arxiv.org/abs/1003.5391

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