2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146180Using Perelman's results on Kahler Ricci flow, we prove that the K energy is bounded from below if and only if the F functional is bounded from below in the canonical Kahler class.Final version, to appear in Osaka Journal of MathematicsDifferential GeometryOn the lower bound of the K energy and F functionaltext