2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144567By establishing the intrinsic super-Poincaré inequality, some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive. These conditions, as well as the resulting uniform upper bounds on the intrinsic heat kernels, are sharp for some concrete examples.Probability60J60; 58G32text