Abstract
Based on a study of the coupling by reflection of diffusion processes, a new monotonicity in time of a time-dependent transportation cost between heat distribution is shown under Bakry-Émery's curvature-dimension condition on a Riemannian manifold. The cost function comes from the total variation between heat distributions on spaceforms. As a corollary, we obtain a comparison theorem for the total variation between heat distributions. In addition, we show that our monotonicity is stable under the Gromov-Hausdorff convergence of the underlying space under a uniform curvature-dimension and diameter bound.
| Original language | English |
|---|---|
| Pages (from-to) | 231-263 |
| Number of pages | 33 |
| Journal | Potential Analysis |
| Volume | 39 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2013 Oct 1 |
Keywords
- Coupling by reflection
- Curvature-dimension condition
- Diffusion process
- Total variation
- Transportation cost
ASJC Scopus subject areas
- Analysis
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Kuwada, K., & Sturm, K. T. (2013). Monotonicity of Time-Dependent Transportation Costs and Coupling by Reflection. Potential Analysis, 39(3), 231-263. https://doi.org/10.1007/s11118-012-9327-4