2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76985We prove an upper bound on the bottom of the essential spectrum of a diffusion in term of the growth of the volume of $X$, generalizing a result by R. Brooks.AMSLaTeX file, 17 pages. Submitted to Comm. PDESpectral TheoryAnalysis of PDEsDifferential Geometrytext