2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168407Let M be a closed Riemannian manifold of dimension n. Let f be an eigenfunction of the Laplace-Beltrami operator corresponding to an eigenvalue λ. We show that the volume of {f>0} inside any ball B whose center lies on {f=0} is > C|B|/λ^n. We apply this result to prove that each nodal domain contains a ball of radius > C/λ^n.12 pages, 1 figure; minor corrections; to appear in Comm. PDEsSpectral TheoryAnalysis of PDEs35P20; 58J50text