Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

Funano, Kei; Sakurai, Yohei

doi:10.1090/proc/14430

Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
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by Kei Funano and Yohei Sakurai PDF

Proc. Amer. Math. Soc. 147 (2019), 3155-3164 Request permission

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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