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arXiv · 1105.4343

Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

Andrea Cianchi·Vladimir Maz'ya
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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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Andrea Cianchi, Vladimir Maz'ya. 2011-05-22. Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds. https://arxiv.org/abs/1105.4343

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