Reference : Exponential contraction in Wasserstein distance on static and evolving manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/42388
Exponential contraction in Wasserstein distance on static and evolving manifolds
English
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]
2021
Revue Roumaine de Mathématiques Pures et Appliquées
Publishing House of the Romanian Academy
66
1
107-129
Yes
International
0035-3965
Bucharest
Romania
[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
http://hdl.handle.net/10993/42388
http://imar.ro/journals/Revue_Mathematique/php/2021/Rrc21_1.php
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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