On Local Poincare via Transportation

Details On Local Poincare via Transportation On Local Poincare via Transportation

2005-05-26

arxiv.org/abs/math/0505588v1

Mathematics

Metric Geometry

Scientific paper

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.

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