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arXiv · 2608.28307

Rigidity of closed $\lambda$-self-expanders

Tongzhu Li·Mengdan Qi
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Abstract

A $\lambda$-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 $\lambda$-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.

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Tongzhu Li, Mengdan Qi. 2026-08-28. Rigidity of closed $\lambda$-self-expanders. https://arxiv.org/abs/2608.28307

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