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Poincaré Inequalities and Uniform Rectifiability (1908.06420v5)
Published 18 Aug 2019 in math.CA, math.DG, and math.MG
Abstract: We show that any $d$-Ahlfors regular subset of $\mathbb{R}{n}$ supporting a weak $(1,d)$-Poincar\'e inequality with respect to surface measure is uniformly rectifiable.