Small eigenvalues of the rough and Hodge Laplacians under fixed volume

For each degree p and each natural number k≥1, we construct on any closed manifold a family of Riemannian metrics, with fixed volume such that the k th positive eigenvalue of the rough or the Hodge Laplacian acting on differential p-forms converges to zero. In particular, on the sphere, we can choose these Riemannian metrics as those of non-negative sectional curvature. This is a generalization of the results by Colbois and Maerten in 2010 to the case of higher degree forms.