Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

Details Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm

2011-11-23

arxiv.org/abs/1111.5526v1

Mathematics

Differential Geometry

25 pages, 1 figure

Scientific paper

We construct geodesics in the Wasserstein space of probability measure along which all the measures have an upper bound on their density that is determined by the densities of the endpoints of the geodesic. Using these geodesics we show that a local Poincar\'e inequality and the measure contraction property follow from the Ricci curvature bounds defined by Sturm. We also show for a large class of convex functionals that a local Poincar\'e inequality is implied by the weak displacement convexity of the functional.

Affiliated with

Also associated with

No associations

Rating

Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Interpolated measures with bounded density in metric spaces satisfying the curvature-dimension conditions of Sturm will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-377480