Dimension-Free Harnack Inequalities on Spaces
Dimension-Free Harnack Inequalities on Spaces
复制标题
空间上的无量纲 Harnack 不等式
DOI：
10.1007/s10959-015-0621-0
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发表时间：
2016
影响因子：
0.8
通讯作者：
Li Huaiqian
中科院分区：
文献类型：
--
作者：
Li Huaiqian
The dimension-free Harnack inequality for the heat semigroup is established on thespace, which is a non-smooth metric measure space having the Ricci curvature bounded from below in the sense of Lott–Sturm–Villani plus the Cheeger energy being quadratic. As its applications, the heat semigroup entropy-cost inequality and contractivity properties of the semigroup are studied, and a strong-enough Gaussian concentration implying the log-Sobolev inequality is also shown as a generalization of the one on the smooth Riemannian manifold.
