PreprintCC BY 4.0arXiv
Any uniformly rectifiable set is contained in a set with Poincaré inequality
Abstract
We show that any uniformly d-rectifiable subset of ℝn is contained in an Ahlfors d-regular set in ℝn+1 which supports a (1,1)-Poincaré inequality. This provides a natural converse to a recent result of Azzam.
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BibTeX
@misc{hyde2026uniformly,
title = {{Any uniformly rectifiable set is contained in a set with Poincaré inequality}},
author = {Matthew Hyde and Michele Villa and Ivan Yuri Violo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03153},
eprint = {2611.03153},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03153},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Any uniformly rectifiable set is contained in a set with Poincaré inequality
AU - Matthew Hyde
AU - Michele Villa
AU - Ivan Yuri Violo
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03153
UR - https://arxiv.org/abs/2611.03153
AB - We show that any uniformly d-rectifiable subset of ℝ^n is contained in an Ahlfors d-regular set in ℝ^n+1 which supports a (1,1)-Poincaré inequality. This provides a natural converse to a recent result of Azzam.
ER -