Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold

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.

11 pages

References in corpus (1)

• Concentration of $1$-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition

Cited by in corpus (1)

• Concentration of $1$-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition