Prescription du spectre du laplacien de Hodge-de Rham dans une classe conforme

Abstract

For any compact manifold of dimension n>=5, we prescribe the volume and any finite part of the spectrum of the Hodge Laplacian acting on diffential forms of degree 1<p<n-1 (exept for p=n/2 if n is even), within a given conformal class. When n<5 and when p=0,1,n-1,n, and p=n/2 if n is even, this simultaneous prescription of the volume, the spectrum and the conformal class is known to be impossible.