PreprintarXiv licencearXiv
Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces
Abstract
We prove that a complete connected scalar-flat Euclidean hypersurface of dimension n≥3 is an affine hyperplane if its normalized mean curvature has sufficiently small Ln norm. We also compute the total mean curvature energy of a classical rotational scalar-flat family to show that finiteness cannot replace smallness in dimensions n≥3.
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BibTeX
@misc{zhou2026total,
title = {{Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces}},
author = {Jiuru Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24653},
eprint = {2610.24653},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24653},
}
RIS
TY - UNPB
TI - Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces
AU - Jiuru Zhou
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24653
UR - https://arxiv.org/abs/2610.24653
AB - We prove that a complete connected scalar-flat Euclidean hypersurface of dimension n≥3 is an affine hyperplane if its normalized mean curvature has sufficiently small L^n norm. We also compute the total mean curvature energy of a classical rotational scalar-flat family to show that finiteness cannot replace smallness in dimensions n≥3.
ER -