Any uniformly rectifiable set is contained in a set with Poincaré inequality
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.
Authors
- Matthew Hyde (ORCID: https://orcid.org/0000-0002-8766-3071)
- Michele Villa (ORCID: https://orcid.org/0000-0002-7702-4698)
- Ivan Yuri Violo (ORCID: https://orcid.org/0000-0001-9592-5150)
Publication Details
- Journal
- arXiv (Cornell University)
- Published
- 2026-11-02
- DOI
- https://doi.org/10.48550/arxiv.2611.03153
- Primary Topic
- Geometric Analysis and Curvature Flows
- Type
- preprint