, Volume 48, Issue 4, pp 547-552

Equivalence of Dimension-Free Harnack Inequality and Curvature Condition

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

Abstract.

Some properties of a diffusion semigroup are proved to be equivalent to the curvature lower bound condition of its generator. In particular, the dimension-free Harnack inequality established in [1] holds if and only if the curvature is bounded below.