2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74926We study strong ratio limit properties and the exact long time asymptotics of the heat kernel of a general second-order parabolic operator which is defined on a noncompact Riemannian manifold.11 pagesAnalysis of PDEsProbability35K10; 35B40; 58J35; 60J60On Davies' conjecture and strong ratio limit properties for the heat kerneltext