Monotonicity of Time-Dependent Transportation Costs and Coupling by Reflection

Kazumasa Kuwada, Karl Theodor Sturm

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)231-263
Number of pages33
JournalPotential Analysis
Volume39
Issue number3
DOIs
Publication statusPublished - 2013 Oct 1

Keywords

  • Coupling by reflection
  • Curvature-dimension condition
  • Diffusion process
  • Total variation
  • Transportation cost

ASJC Scopus subject areas

  • Analysis

Fingerprint Dive into the research topics of 'Monotonicity of Time-Dependent Transportation Costs and Coupling by Reflection'. Together they form a unique fingerprint.

  • Cite this