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Let us consider a riemannian vector bundle E with compact basis (M,g) and the rough laplacian Δ associated to a connection D on E. We prove that the eigenvalues of Δ 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.

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