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arXiv · 2610.24653

Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces

Jiuru Zhou
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Abstract

We prove that a complete connected scalar-flat Euclidean hypersurface of dimension $n\geq3$ 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 $n\geq3$.

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Jiuru Zhou. 2026-10-17. Total Mean Curvature Gaps for Scalar-Flat Hypersurfaces. https://arxiv.org/abs/2610.24653

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