A closed d-Ahlfors regular set in R^n supporting a weak (1,d)-Poincaré inequality is uniformly d-rectifiable for d >= 2.
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Poincar\'e Inequalities and Uniform Rectifiability
A closed d-Ahlfors regular set in R^n supporting a weak (1,d)-Poincaré inequality is uniformly d-rectifiable for d >= 2.