Gradient Estimate and Harnack Inequality on Non-Compact Riemannian Manifolds
by Marc Arnaudon, Anton Thalmaier and Feng-Yu Wang

A new type of gradient estimate is established for diffusion semigroups on non-compact complete Riemannian manifolds. As applications, a global Harnack inequality with power and a heat kernel estimate are derived for diffusion semigroups on arbitrary complete Riemannian manifolds.

Stochastic Processes Appl. 119 (2009) 3653-3670
doi 10.1016/

The paper is available here:

Marc Arnaudon
Anton Thalmaier
Feng-Yu Wang

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