AI 中文总结
本文研究闭λ-自展形的刚性问题，证明在标量曲率、平均曲率及第二基本形式平方范数等曲率条件下，闭λ-自展形为中心在原点的圆球面。
AI 中文摘要
λ-自展形$x: M^n\to \mathbb{R}^{n+1}$是权重为$e^{\frac{|x|^2}{4}}$的等周问题的解。本文证明，在标量曲率、平均曲率及第二基本形式的平方范数等曲率条件下，闭λ-自展形是中心在原点的圆球面。
英文摘要
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.
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