Harnack Inequality and Heat Kernel Estimates on Manifolds with Curvature Unbounded Below
by Marc Arnaudon, Anton Thalmaier and Feng-Yu Wang

Using the coupling by parallel translation, along with Girsanov's theorem, a new version of a dimension-free Harnack inequality is established for diffusion semigroups on Riemannian manifolds with Ricci curvature bounded below by -c (1+ρ2) , where c > 0 is a constant and  ρ  is the Riemannian distance function to a fixed point  ο  on the manifold. As an application, in the symmetric case, a Li-Yau type heat kernel bound is presented for such semigroups.

Bull. Sci. Math. 130  (2006)  223-233  [ORIGINAL ARTICLE]

The paper is available here:

Marc Arnaudon
Anton Thalmaier
Feng-Yu Wang

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