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

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