Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Kei Funano; Yohei Sakurai

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arXiv · 1712.09084

Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Kei Funano·Yohei Sakurai

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Abstract

We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequalities and restricted Sogge-type $L_p$ moment estimates of eigenfunctions.

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BibTeX RIS

Kei Funano, Yohei Sakurai. 2019-01-10. Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold. https://arxiv.org/abs/1712.09084

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