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arXiv · 2607.27114

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

Aritro Pathak
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Abstract

We resolve a conjecture of Guy David and Svitlana Mayboroda. We show that if $\Omega \subset \mathbb{R}^n$ is a uniform domain with $(n-1)$-dimensional Ahlfors David regular boundary $E = \partial \Omega$, 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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Aritro Pathak. 2026-07-29. Weak geometric lemma for ADR boundary of a uniform domain implies uniform rectifiability. https://arxiv.org/abs/2607.27114

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