Monotonicity of Time-Dependent Transportation Costs and Coupling by Reflection

Kazumasa Kuwada, Karl Theodor Sturm

研究成果: Article査読

3 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)231-263
ページ数33
ジャーナルPotential Analysis
39
3
DOI
出版ステータスPublished - 2013 10

ASJC Scopus subject areas

  • 分析

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