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On Local Poincare via Transportation

Max-K. von Renesse
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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.

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Max-K. von Renesse. 2005-05-26. On Local Poincare via Transportation. https://arxiv.org/abs/math/0505588

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