Institut de Mathématiques de Bordeaux, Laboratoire d'Analyse et Géométrie, UMR 5467, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence, France
Abstract:
We consider general Schrödinger operators on domains of Riemannian manifolds with possibly exponential volume growth. We prove sharp large time Gaussian upper bounds. These bounds are then used to prove new Lp-Lp estimates for the corresponding semigroups. Applications to semi-linear parabolic equations are given.