Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound

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 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.
Document type :
Journal articles
Liste complète des métadonnées

Cited literature [13 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01057529
Contributor : Marc Arnaudon <>
Submitted on : Saturday, August 23, 2014 - 1:14:00 AM
Last modification on : Wednesday, November 21, 2018 - 5:52:06 PM
Document(s) archivé(s) le : Thursday, November 27, 2014 - 1:56:04 PM

File

12atw.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01057529, version 1

Collections

Citation

Marc Arnaudon, Anton Thalmaier, Feng-Yu Wang. Equivalent Harnack and Gradient Inequalities for Pointwise Curvature Lower Bound. Bulletin des Sciences Mathématiques, Elsevier, 2014, 138 (5), pp.643-655. ⟨hal-01057529⟩

Share

Metrics

Record views

153

Files downloads

122