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 |
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Pages (from-to) | 231-263 |
Number of pages | 33 |
Journal | Potential Analysis |
Volume | 39 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2013 Oct |
Keywords
- Coupling by reflection
- Curvature-dimension condition
- Diffusion process
- Total variation
- Transportation cost
ASJC Scopus subject areas
- Analysis