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ISSN 1088-6850(e) ISSN 0002-9947(p)

Sur la multiplicité des valeurs propres du Laplacien de Witten

Author: Pierre Jammes
Journal: Trans. Amer. Math. Soc. 364 (2012), 2825-2845
MSC (2010): Primary 58J50
Posted: January 31, 2012
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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 -form for . 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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