Une inégalité du type Payne-Polya-Weinberger pour le laplacien brut
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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 $D$.References
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Additional Information
- Bruno Colbois
- Affiliation: Institut de Mathématiques, Université de Neuchâtel, CH-2007 Neuchâtel, Switzerland
- MR Author ID: 50460
- Email: bruno.colbois@unine.ch
- Received by editor(s): July 6, 2002
- Published electronically: April 30, 2003
- Communicated by: Jozef Dodziuk
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3937-3944
- MSC (2000): Primary 58J50; Secondary 35P15
- DOI: https://doi.org/10.1090/S0002-9939-03-07056-4
- MathSciNet review: 1999944