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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Une inégalité du type Payne-Polya-Weinberger pour le laplacien brut


Author: Bruno Colbois
Journal: Proc. Amer. Math. Soc. 131 (2003), 3937-3944
MSC (2000): Primary 58J50; Secondary 35P15
Published electronically: April 30, 2003
MathSciNet review: 1999944
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Abstract: Let us consider a riemannian vector bundle $E$ with compact basis $(M,g)$ and the rough laplacian $\bar{\Delta}$ associated to a connection $D$ on $E$. We prove that the eigenvalues of $\bar{\Delta}$ are bounded above by a function of the first eigenvalue and of the geometry of $(M,g)$, but independently of the choice of the connection $D$.


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Additional Information

Bruno Colbois
Affiliation: Institut de Mathématiques, Université de Neuchâtel, CH-2007 Neuchâtel, Switzerland
Email: bruno.colbois@unine.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07056-4
PII: S 0002-9939(03)07056-4
Keywords: Rough Laplacian, spectrum, Riemannian bundle
Received by editor(s): July 6, 2002
Published electronically: April 30, 2003
Communicated by: Jozef Dodziuk
Article copyright: © Copyright 2003 American Mathematical Society