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Lawlor's curvature criterion and topologically trivial area-minimizing hypercones of Hsiang type
Abstract
For a closed embedded minimal hypersurface in a unit sphere, we show that the existence of a uniform vanishing angle in Lawlor's criterion suffices for its cone to minimize area. The normal-wedge condition follows from Howard's rolling theorem. We derive explicit curvature bounds and apply them to the reported Hsiang-Sterling curvature estimates for topologically trivial cones. The resulting area-minimizing cones give an affirmative answer to the existence question raised by Ilmanen and White (Camb. J. Math., 2015).
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BibTeX
@misc{cui2026lawlors,
title = {{Lawlor's curvature criterion and topologically trivial area-minimizing hypercones of Hsiang type}},
author = {Hongbin Cui},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31341},
eprint = {2610.31341},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31341},
}
RIS
TY - UNPB
TI - Lawlor's curvature criterion and topologically trivial area-minimizing hypercones of Hsiang type
AU - Hongbin Cui
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31341
UR - https://arxiv.org/abs/2610.31341
AB - For a closed embedded minimal hypersurface in a unit sphere, we show that the existence of a uniform vanishing angle in Lawlor's criterion suffices for its cone to minimize area. The normal-wedge condition follows from Howard's rolling theorem. We derive explicit curvature bounds and apply them to the reported Hsiang-Sterling curvature estimates for topologically trivial cones. The resulting area-minimizing cones give an affirmative answer to the existence question raised by Ilmanen and White (Camb. J. Math., 2015).
ER -