On Local Poincare via Transportation
Metric Geometry
2007-05-23 v1 Differential Geometry
Abstract
It is shown that curvature-dimension bounds CD(N, k) for a metric measure space (X,d,m) in the sense of Sturm imply a weak L^1- Poincare-inequality under some symmetry assumption on the choice of transport rays in the cut locus of (X,d). This condition is satisfied if (X,d) has m-almost surely no branching points.
Cite
@article{arxiv.math/0505588,
title = {On Local Poincare via Transportation},
author = {Max-K. von Renesse},
journal= {arXiv preprint arXiv:math/0505588},
year = {2007}
}