Abstract

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 $M$.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 579-635
Launched on MUSE
2013-05-30
Open Access
No
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