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

Aritro Pathak

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

Classical Analysis and ODEs 2026-07-29 v1

Authors: Aritro Pathak

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.

Keywords

uniform domain Ahlfors David regular weak geometric lemma bilateral weak geometric lemma uniform rectifiability

Cite

@article{arxiv.2607.27114,
  title  = {Weak geometric lemma for ADR boundary of a uniform domain implies uniform rectifiability},
  author = {Aritro Pathak},
  journal= {arXiv preprint arXiv:2607.27114},
  year   = {2026}
}

Comments

10 pages, 1 figure