On the essential spectrum of the Laplacian and vague convergence of the curvature at infinity

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75306We shall prove that under some volume growth condition, the essential spectrum of the Laplacian contains the interval $[(n-1)^2K/4, \infty)$ if an $n$-dimensional Riemannian manifold has an end and the average of the part of the Ricci curvature on the end which lies below a nonpositive constant $(n-1)K$ converges to zero at infinity.12 pagesDifferential GeometrySpectral Theory58J50; 53C20; 35P05On the essential spectrum of the Laplacian and vague convergence of the curvature at infinitytext