RCD（K，\infty）度量测度空间中热流的Bakry-Émery条件和Wasserstein收缩
Self-improvement of the Bakry-Émery condition and Wasserstein contraction of the heat flow in RCD(K,\infty) metric measure spaces
摘要：
本文证明了RCD（K，\infty）度量测度空间（X，d，m）中的线性热流关于每个L^p-Kantorovich-Rubinstein-Wasserstein距离都满足收缩性质.特别地，我们得到了两个基本解之间的最优W_ \infty -耦合关于初始点距离的精确估计.这个结果是（X，d，m）中正则Cheeger-Dirichlet型的RCD（K，\infty）Ricci下界与相应的Bakry-Émery条件之间等价的结果.关键的工具是扩展到非光滑的度量措施设置的巴克里的论点，这使得能够提高之间的交换估计的马尔可夫半群和Carré du Champ相关联的狄利克雷形式。这种扩展是基于一个新的先验估计和一个容量参数的定期和紧狄利克雷形式是独立的利益。
英文摘要：
We prove that the linear heat flow in a RCD(K,\infty) metric measure space (X,d,m) satisfies a contraction property with respect to every L^p-Kantorovich-Rubinstein-Wasserstein distance. In particular, we obtain a precise estimate for the optimal W_\infty-coupling between two fundamental solutions in terms of the distance of the initial points. The result is a consequence of the equivalence between the RCD(K,\infty) lower Ricci bound and the corresponding Bakry-Émery condition for the canonical Cheeger-Dirichlet form in (X,d,m). The crucial tool is the extension to the non-smooth metric measure setting of the Bakry's argument, that allows to improve the commutation estimates between the Markov semigroup and the Carré du Champ associated to the Dirichlet form. This extension is based on a new a priori estimate and a capacitary argument for regular and tight Dirichlet forms that are of independent interest.
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