Remote Access Transactions of the American Mathematical Society
Green Open Access

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
MathSciNet review: 2888230
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 58J50

Retrieve articles in all journals with MSC (2010): 58J50

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

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.

American Mathematical Society