  This paper shows that when the Riemannian metric on a contact manifold is
blown up along the direction orthogonal to the contact distribution, the
corresponding harmonic forms rescaled and normalized in the $L^2$-norms will
converge to Rumin's harmonic forms. This proves a conjecture in Gromov ``
Carnot-Caratheodory spaces seen from within '', IHES preprint, 1994. This
result can also be reformulated in terms of spectral sequences, after Forman,
Mazzeo-Melrose. A key ingredient in the proof is the fact that the curvatures
become unbounded in a controlled way.
