Year: 2026
Type: preprint
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 $n\geq3$.
Source: arXiv (Cornell University)
Author: Zhou, Jiuru
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223055008