Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

We deal with eigenvalue problems for the Laplacian on noncompact Riemannian manifolds M of finite volume. Sharp conditions ensuring L^q(M) and L^∞(M) bounds for eigenfunctions are exhibited in terms of either the isoperimetric function or the isocapacitary function of M. The research that led to the present paper was partially supported by a grant of the group GNAMPA of INdAM.