[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 :
Mathématiques
Auteur, co-auteur :
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
Co-auteurs externes :
yes
Langue du document :
Anglais
Titre :
Exponential contraction in Wasserstein distance on static and evolving manifolds
Date de publication/diffusion :
2021
Titre du périodique :
Revue Roumaine de Mathématiques Pures et Appliquées
ISSN :
0035-3965
Maison d'édition :
Publishing House of the Romanian Academy, Bucharest, Roumanie
