Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

Details Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

2011-05-22

arxiv.org/abs/1105.4343v1

Mathematics

Analysis of PDEs

48 pages, 3 figures

Scientific paper

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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