Concentration of eigenfunctions of the Laplacian on a closed Riemannian manifold
Kei Funano, Yohei Sakurai · Proceedings of the American Mathematical Society · 2018
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.