Exponential
contraction in Wasserstein distance on static and evolving
manifolds
by Li-Juan Cheng, Anton Thalmaier and Shao-Qin Zhang
Abstract
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.
Rev. Roumaine Math. Pures Appl. 66 (2021), no. 1, 107-129
The paper is available here:
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