论文标题
在静态和不断发展的歧管上的Wasserstein距离中的指数收缩
Exponential contraction in Wasserstein distance on static and evolving manifolds
论文作者
论文摘要
在本文中，在Riemannian歧管上扩散过程的Wasserstein距离的指数收缩是在曲率条件下建立的，而RICCI曲率不一定必须是非负的。与Wang（2016）的结果相比，我们专注于指数收缩率的明确估计。此外，我们表明我们的结果扩展到在几何流动下演变的歧管。作为应用，对于时间不均匀的半群，我们在弱曲率条件下获得了指数收缩率的梯度估计，以及相应的措施演化系统的唯一性。
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.
