PreprintarXiv licencearXiv
A Generalized Lai--Wei Construction and New Families of Area-Minimizing Hypercones
Abstract
Our results are twofold. Inspired by recent work on weighted spheres, we extend the Lai--Wei construction from one to several independent isoparametric inputs, replacing its profile curve by a hypersurface profile to generate minimal hypersurfaces in spheres. Using a curvature criterion, we obtain new infinite families of area-minimizing hypercones from the original construction and its extensions.
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BibTeX
@misc{zhang2026generalized,
title = {{A Generalized Lai--Wei Construction and New Families of Area-Minimizing Hypercones}},
author = {Yongsheng Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05149},
eprint = {2611.05149},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05149},
}
RIS
TY - UNPB
TI - A Generalized Lai--Wei Construction and New Families of Area-Minimizing Hypercones
AU - Yongsheng Zhang
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05149
UR - https://arxiv.org/abs/2611.05149
AB - Our results are twofold. Inspired by recent work on weighted spheres, we extend the Lai--Wei construction from one to several independent isoparametric inputs, replacing its profile curve by a hypersurface profile to generate minimal hypersurfaces in spheres. Using a curvature criterion, we obtain new infinite families of area-minimizing hypercones from the original construction and its extensions.
ER -