Reference : Exponential contraction in Wasserstein distance on static and evolving manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Exponential contraction in Wasserstein distance on static and evolving manifolds
Cheng, Li Juan [Zhejiang University of Technology > Department of Applied Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Zhang, Shao-Qin [Central University of Finance and Economics, Beijing > School of Applied Mathematics]
Revue Roumaine de Mathématiques Pures et Appliquées
Publishing House of the Romanian Academy
[en] In this article, exponential contraction in Wasserstein distance for heat semigroups of diffusion processes on Riemannian manifolds is established under curvature conditions where Ricci curvature is not necessarily required to be non-negative. Compared to the results of Wang (2016), we focus on explicit estimates for the exponential contraction rate. Moreover, we show that our results extend to manifolds evolving under a geometric flow. As application, for the time-inhomogeneous semigroups, we obtain a gradient estimate with an exponential contraction rate under weak curvature conditions, as well as uniqueness of the corresponding evolution system of measures.
R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton
Researchers ; Students
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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