Equivalent Semigroup Properties for Curvature-Dimension Condition

2010/12/28 by Feng-Yu Wang, Wang, Feng-Yu · 1 citation
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1012.5686

16 pages

arxiv created 2010/12/28 · arxiv updated 2010/12/30

Abstract

Some equivalent gradient and Harnack inequalities of a diffusion semigroup are presented for the curvature-dimension condition of the associated generator. As applications, the first eigenvalue, the log-Harnack inequality, the heat kernel estimates, and the HWI inequality are derived by using the curvature-dimension condition. The transportation inequality for diffusion semigroups is also investigated.

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