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arXiv · 2611.03153

Any uniformly rectifiable set is contained in a set with Poincaré inequality

Matthew Hyde·Michele Villa·Ivan Yuri Violo
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Abstract

We show that any uniformly $d$-rectifiable subset of $\mathbb{R}^n$ is contained in an Ahlfors $d$-regular set in $\mathbb{R}^{n+1}$ which supports a $(1,1)$-Poincaré inequality. This provides a natural converse to a recent result of Azzam.

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Matthew Hyde, Michele Villa, Ivan Yuri Violo. 2026-11-02. Any uniformly rectifiable set is contained in a set with Poincaré inequality. https://arxiv.org/abs/2611.03153

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