Riemannian metrics with large first eigenvalue on forms of degree $p$

Let (M, g) be a compact, connected, CO Riemannian manifold of n dimensions. Denote by RI ,p(M, g) the first nonzero eigenvalue of the Laplace operator acting on differential forms of degree p. We prove that for n > 4 and 2 < p < n 2, there exists a family of metrics gt of volume one, suchthat AI ,p(M,gt) -+oo as t -+oo.