Prescription de la multiplicité des valeurs propres du laplacien de Hodge–de Rham

Abstract

On any compact manifold of dimension greater than 6, we prescribe the volume and any finite part of the spectrum of the Hodge Laplacian acting on $p$-form for $1\le p<\frac{n}{2}$. In particular, we prescribe the multiplicity of the first eigenvalues.