In this paper, We define a $\mathcal{F}$-functional and study $\mathcal{F}$-stability of $\lambda$-hypersurfaces, which extend a result of Colding–Minicozzi [6]. Lower bound growth and upper bound growth of area for complete and non-compact $\lambda$-hypersurfaces are studied.

中文翻译：

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$\lambda$-超曲面的稳定性和面积增长

在本文中，我们定义了一个 $\mathcal{F}$-泛函并研究了 $\lambda$-超曲面的 $\mathcal{F}$-稳定性，它扩展了 Colding–Minicozzi [6] 的结果。研究了完整和非紧凑 $\lambda$ 超曲面的面积下限增长和上限增长。