Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound
by Marc Arnaudon, Anton Thalmaier and Feng-Yu Wang

By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) diffusion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the consequent L²-gradient inequality, are proved to be equivalent to the pointwise curvature lower bound condition together with the convexity or absence of the boundary. Some applications of the log-Harnack inequality are also introduced.

Bull. Sci. Math. 138  (2014) 643-655  [ORIGINAL ARTICLE]


The paper is available here:

Marc Arnaudon
Anton Thalmaier
Feng-Yu Wang

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