Year: 2026
Type: preprint
Abstract: A $λ$-self-expander $x: M^n\to \mathbb{R}^{n+1}$ is the solution of the isoperimetric problem of weight $e^{\frac{|x|^2}{4}}$. In this paper, we prove that the closed $λ$-self-expander is a round sphere centered at the origin under some curvature conditions. These curvature conditions mainly include the scalar curvature, the mean curvature, and the squared norm of the second fundamental form.
Source: arXiv (Cornell University)
Authors: Li, Tongzhu, Qi, Mengdan
Institution: Beijing Institute of Technology
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2131439191
OpenAlex ID: W7204972589
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