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Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 3, June 2013
- pp. 579-635
- 10.1353/ajm.2013.0028
- Article
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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 $M$.