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Let,  n ≥2, be a closed, Ahlfors–David regular set of dimension  n  satisfying the “Riesz Transform bound”Assume further that  E  is the boundary of a domainsatisfying the Harnack Chain condition plus an interior (but not exterior) corkscrew condition. Then  E  is uniformly rectifiable.

Uniform Rectifiability and Harmonic Measure III: Riesz Transform Bounds Imply Uniform Rectifiability of Boundaries of 1-sided NTA Domains