Equivalent Semigroup Properties for Curvature-Dimension Condition

Details Equivalent Semigroup Properties for Curvature-Dimension Condition Equivalent Semigroup Properties for Curvature-Dimension Condition

2010-12-28

arxiv.org/abs/1012.5686v1

Mathematics

Probability

16 pages

Scientific paper

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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