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arXiv · 2605.29804

On the WALA conjecture, Alberti representations and applications

Andrea Merlo
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Abstract

We prove the WALA conjecture of G. David and S. Semmes: every AD-regular Radon measure for which all real-valued Lipschitz functions satisfy the weak approximation by affine functions condition is uniformly rectifiable. In order to prove the conjecture, we identify the correct quantitative analogue of the decomposability bundle and establish several structural results for general AD-regular measures.

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Andrea Merlo. 2026-05-28. On the WALA conjecture, Alberti representations and applications. https://arxiv.org/abs/2605.29804

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