Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds
Andrea Cianchi, Vladimir Gilelevich Maz'ya · arXiv (Cornell University) · 2011
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 $M$.