Dimension-Free Harnack Inequalities on $$\hbox {RCD}(K, \infty )$$ RCD ( K, ∞ ) Spaces

Huaiqian Li ()
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Huaiqian Li: Sichuan University

Journal of Theoretical Probability, 2016, vol. 29, issue 4, 1280-1297

Abstract: Abstract The dimension-free Harnack inequality for the heat semigroup is established on the $$\mathrm{{RCD}}(K,\infty )$$ RCD ( K , ∞ ) space, 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.

Keywords: Harnack inequality; Heat semigroup; Metric measure space; Riemannian curvature; 60J60; 31C25; 49J52; 47D07 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-015-0621-0

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