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arXiv · 2310.02938

Some universal inequalities of eigenvalues and upper bounds for the $L_{\infty}$ norm of eigenfunctions of the Laplacian

Kei Funano
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Abstract

In this short survey, we derive some weyl-type universal inequalities of eigenvalues of the Laplacian on a closed Riemannian manifold of nonnegative Ricci curvature. We also give upper bounds for the $L_{\infty}$ norm of eigenfunctions of the Laplacian in the same setting. A detailed proof of these results did not seem to appear in the literature but the results follow from a simple combination of Milman's work and Cheng-Li's work.

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Kei Funano. 2023-10-04. Some universal inequalities of eigenvalues and upper bounds for the $L_{\infty}$ norm of eigenfunctions of the Laplacian. https://arxiv.org/abs/2310.02938

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