  For each degree p, we construct on any closed manifold a family of Riemannian
metrics, with fixed volume such that any positive eigenvalues of the rough and
Hodge Laplacians acting on differential p-forms converge 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.
