PreprintCC BY-NC-ND 4.0arXiv
Sobolev homeomorphisms and Jordan curves with positive area
Abstract
Each homeomorphic parametrization of a Jordan curve via the unit circle πβ π2 extends to a homeomorphism of the entire π2. We show that there exists a Jordan curve of positive area whose every parametrization via π admits a homeomorphic extension that has p-Sobolev regularity on π2 for all exponents 1β€ p<2 . This is obtained via a new sharp extension result for the case of p<2.
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BibTeX
@misc{koskela2026sobolev,
title = {{Sobolev homeomorphisms and Jordan curves with positive area}},
author = {Pekka Koskela and Haiqing Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07322},
eprint = {2611.07322},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07322},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Sobolev homeomorphisms and Jordan curves with positive area
AU - Pekka Koskela
AU - Haiqing Xu
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07322
UR - https://arxiv.org/abs/2611.07322
AB - Each homeomorphic parametrization of a Jordan curve via the unit circle πβ π^2 extends to a homeomorphism of the entire π^2. We show that there exists a Jordan curve of positive area whose every parametrization via π admits a homeomorphic extension that has p-Sobolev regularity on π^2 for all exponents 1β€ p<2 . This is obtained via a new sharp extension result for the case of p<2.
ER -