PUB - Publikationen an der Universität Bielefeld

Under a curvature condition, we obtain some criteria of supercontractivity and ultracontractivity for (non-symmetric) diffusion semigroups on Riemannian manifolds. As consequences, some sufficient and necessary conditions are presented for these two contraction properties. Then, based on a perturbation argument, ultracontractivity is studied for symmetric diffusions with non-smooth drifts. Moreover, we provide a way to study contraction properties using isoperimetric inequalities. To illustrate the main results, some typical examples are constructed, where one of them shows that supercontractivity is strictly weaker than ultracontractivity as already known in the flat case.