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On the measure of the boundary of a Hajłasz-Sobolev (M1,p,M1,q)-extension domain
Abstract
We prove that the boundary of every bounded (M1,p,M1,q)-extension domain in a Q-doubling metric measure space has measure zero whenever 0<q<p<∞, with the additional restriction that p<qQ/(Q−q) if q<Q.
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BibTeX
@misc{alvarado2026measure,
title = {{On the measure of the boundary of a Hajłasz-Sobolev $(M^1,p,M^1,q)$-extension domain}},
author = {Ryan Alvarado and Riddhi Mishra},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.28807},
eprint = {2608.28807},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.28807},
}
RIS
TY - UNPB
TI - On the measure of the boundary of a Hajłasz-Sobolev (M^1,p,M^1,q)-extension domain
AU - Ryan Alvarado
AU - Riddhi Mishra
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2608.28807
UR - https://arxiv.org/abs/2608.28807
AB - We prove that the boundary of every bounded (M^1,p,M^1,q)-extension domain in a Q-doubling metric measure space has measure zero whenever 0<q<p<∞, with the additional restriction that p<qQ/(Q−q) if q<Q.
ER -