Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

Andrea Cianchi; Vladimir Maz'ya

Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds

Analysis of PDEs 2011-05-24 v1

Authors: Andrea Cianchi , Vladimir Maz'ya

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 $M$ .

Keywords

eigenfunctions Laplacian noncompact Riemannian manifolds finite volume L^q bounds L^∞ bounds isoperimetric function isocapacitary function

Cite

@article{arxiv.1105.4343,
  title  = {Bounds for eigenfunctions of the Laplacian on noncompact Riemannian manifolds},
  author = {Andrea Cianchi and Vladimir Maz'ya},
  journal= {arXiv preprint arXiv:1105.4343},
  year   = {2011}
}

Comments

48 pages, 3 figures

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