David–Mayboroda conjecture on the weak geometric lemma for uniform domains

Let $\Omega \subset \mathbb{R}^n$ be a domain with boundary $E = \partial \Omega$. Assume that $E$ is $(n-1)$-dimensional Ahlfors–David regular, and that $\Omega$ is a uniform domain. If $E$ satisfies the Weak Geometric Lemma, then $E$ satisfies the Bilateral Weak Geometric Lemma, and hence is uniformly rectifiable.

David–Mayboroda conjecture. Under these hypotheses, the Weak Geometric Lemma implies the Bilateral Weak Geometric Lemma, and consequently uniform rectifiability of $E$.

The conjecture concerns quantitative rectifiability of boundaries of uniform domains. The paper's abstract states that it resolves the conjecture affirmatively, so the claim is now established.