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Dimension-Free Harnack Inequality and its Applications

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Abstract

This paper presents a self-contained account concerning a dimension-free Harnack inequality and its applications. This new type of inequality not only implies heat kernel bounds as the classical Li-Yau’s Harnack inequality did, but also provides a direct way to describe various dimension-free properties of finite and infinite-dimensional diffusion semigroups. The author starts with a standard weighted Laplace operator on a Riemannian manifold with curvature bounded from below, and then move further to the unbounded below curvature case and its infinite-dimensional settings.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Wang Feng-Yu

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

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Wang, FY. Dimension-Free Harnack Inequality and its Applications. Front. Math. China 1, 53–72 (2006). https://doi.org/10.1007/s11464-005-0021-3

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  • DOI: https://doi.org/10.1007/s11464-005-0021-3

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