  We show that a noncompact manifold with bounded sectional curvature, whose
ends are sufficiently Gromov-Hausdorff close to rays, has a finite dimensional
space of square-integrable harmonic forms. In the special case of a
finite-volume manifold with pinched negative sectional curvature, we show that
the essential spectrum of the p-form Laplacian is the union of the essential
spectra of a collection of ordinary differential operators associated to the
ends. We give examples of such manifolds with curvature pinched arbitrarily
close to -1 and with an infinite number of gaps in the spectrum of the function
Laplacian.
