2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105143We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.17 pages, 1 figure, submitted for publicationSpectral TheoryAnalysis of PDEsFunctional Analysis58J50; 35J70text