  Given a closed Riemannian manifold of dimenion less than eight, we prove a
compactness result for the space of closed, embedded minimal hypersurfaces
satisfying a volume bound and a uniform lower bound on the first eigenvalue of
the stability operator. When the latter assumption is replaced by a uniform
lower bound on the p-th Jacobi eigenvalue for p greater or equal than 2 one
gains strong convergence to a smooth limit submanifold away from at most p-1
points.
