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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+ρ^{2}) , 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

The paper is available here:

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