On Local Poincare via Transportation

2005/05/26 by Max‐K. von Renesse, Max-K. von Renesse, von Renesse, Max-K. · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG #math.MG

paper · pdf · doi:10.48550/arxiv.math/0505588

arxiv created 2005/05/26 · arxiv updated 2009/12/01

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 L¹- 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.

Citations

• Lower Bounds on Ricci Curvature and the Almost Rigidity of Warped Products

Cited by

• On the Structure of Busemann Spaces with Non-Negative Curvature

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