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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: 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 $ 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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Additional Information

Pierre Jammes
Affiliation: Laboratoire d’analyse non linéaire et géométrie (EA 2151), Université d’Avignon et des pays de Vaucluse, F-84018 Avignon cedex 1, France
Email: pierre.jammes@ens-lyon.org

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05363-3
PII: S 0002-9947(2012)05363-3
Keywords: Witten Laplacian, differential forms, multiplicity of eigenvalues
Received by editor(s): March 29, 2010
Published electronically: January 31, 2012
Additional Notes: The author benefited from the ANR grant Geodycos ANR-07-BLAN-0140-01
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.