PreprintCC BY 4.0arXiv
On Simon's area-minimizing hypersurfaces with fractal singular sets
Abstract
We verify that the stable minimal hypersurfaces with prescribed singular sets constructed by Leon Simon are area-minimizing. Thus, Simon's work settles the existence of area-minimizing hypersurfaces with fractal singular sets.
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BibTeX
@misc{liu2026simons,
title = {{On Simon's area-minimizing hypersurfaces with fractal singular sets}},
author = {Zhenhua Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31615},
eprint = {2609.31615},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31615},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On Simon's area-minimizing hypersurfaces with fractal singular sets
AU - Zhenhua Liu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.31615
UR - https://arxiv.org/abs/2609.31615
AB - We verify that the stable minimal hypersurfaces with prescribed singular sets constructed by Leon Simon are area-minimizing. Thus, Simon's work settles the existence of area-minimizing hypersurfaces with fractal singular sets.
ER -