[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.
Disciplines :
Mathematics
Author, co-author :
CHENG, Li Juan ; Zhejiang University of Technology > Department of Applied Mathematics
THALMAIER, Anton ; 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
External co-authors :
yes
Language :
English
Title :
Exponential contraction in Wasserstein distance on static and evolving manifolds
Publication date :
2021
Journal title :
Revue Roumaine de Mathématiques Pures et Appliquées
ISSN :
0035-3965
Publisher :
Publishing House of the Romanian Academy, Bucharest, Romania