Monotonicity of time-dependent transportation costs and coupling by reflection

Kazumasa Kuwada; Karl-Theodor Sturm

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arXiv · 1204.3232

Monotonicity of time-dependent transportation costs and coupling by reflection

Kazumasa Kuwada·Karl-Theodor Sturm

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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-Emery'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.

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BibTeX RIS

Kazumasa Kuwada, Karl-Theodor Sturm. 2012-04-15. Monotonicity of time-dependent transportation costs and coupling by reflection. https://arxiv.org/abs/1204.3232

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