Equivalence of Dimension-Free Harnack Inequality and Curvature Condition
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- Wang, FY. Integr. equ. oper. theory (2004) 48: 547. doi:10.1007/s00020-002-1264-y
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Some properties of a diffusion semigroup are proved to be equivalent to the curvature lower bound condition of its generator. In particular, the dimension-free Harnack inequality established in  holds if and only if the curvature is bounded below.