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Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound
Language
en
Article de revue
This item was published in
Bulletin des Sciences Mathématiques. 2014-07-01, vol. 138, n° 5, p. 643-655
Elsevier
English Abstract
By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) di usion semigroups on a Riemannian manifold (possibly with boundary). This inequality as ...Read more >
By using a coupling method, an explicit log-Harnack inequality with local geometry quantities is established for (sub-Markovian) di usion semigroups on a Riemannian manifold (possibly with boundary). This inequality as well as the consequent L^2 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.Read less <
English Keywords
Log-Harnack inequality
Riemannian manifold
diffusion process
Origin
Hal imported