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Equivalence of Dimension-Free Harnack Inequality and Curvature Condition

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Abstract.

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 [1] holds if and only if the curvature is bounded below.

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  1. Department of Mathematics, Beijing Normal University, Beijing, 100875, China

    Feng-Yu Wang

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  1. Feng-Yu Wang
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Correspondence to Feng-Yu Wang.

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Wang, FY. Equivalence of Dimension-Free Harnack Inequality and Curvature Condition. Integr. equ. oper. theory 48, 547–552 (2004). https://doi.org/10.1007/s00020-002-1264-y

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  • DOI: https://doi.org/10.1007/s00020-002-1264-y

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