Weak geometric lemma for ADR boundary of a uniform domain implies uniform rectifiability

2026/07/29 by Aritro Pathak
Mathematics · #math.CA

paper · pdf

11 pages, 1 figure; minor correction of the εprefactor in the proof

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We resolve a conjecture of Guy David and Svitlana Mayboroda. We show that if Ω⊂ ℝⁿ is a uniform domain with (n-1)-dimensional Ahlfors David regular boundary E = ∂ Ω, and if E satisfies the Weak Geometric Lemma, then E satisfies the Bilateral Weak Geometric Lemma. In particular, E is uniformly rectifiable.

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