The spectrum of the Hodge Laplacian for a degenerating family of hyperbolic three manifolds

We consider a sequence (M")^=i of compact hyperbolic manifolds converging to a complete hyperbolic manifold Mq with cusps. The Laplace operator acting on the space of L2 differential forms on M0 has continuous spectrum filling the half-line (0, oo). One expects therefore that the spectra of this operator on M" accumulate to produce the continuous spectrum of the limiting manifold. We prove that this is the case and obtain a sharp estimate of the rate of accumulation.