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 $L^\infty (M)$ bounds for eigenfunctions are exhibited in terms of either the isoperimetric function or the isocapacitary function of $M$. 
Andrea Cianchi, Vladimir Maz'ya
math.AP