论文标题
$λ$ - 自行超越者的一些刚性属性
Some rigidity properties for $λ$-self-expanders
论文作者
论文摘要
$λ$ - expanders $σ$ in $ \ mathbb {r}^{n+1} $是相对于自我膨胀者研究中相同的加权区域形式的等值问题的解决方案。在本文中，我们主要将结果扩展到我们在\ cite {ancari2020volum}中获得的自膨胀者，到$λ$ - self-expanders。我们证明了一些将超平面，球体和圆柱体的表征为$λ$ - 自我膨胀者的结果。我们还讨论了在平均曲率生长的控制下，加权区域的生长和有限。
$λ$-self-expanders $Σ$ in $\mathbb{R}^{n+1}$ are the solutions of the isoperimetric problem with respect to the same weighted area form as in the study of the self-expanders. In this paper, we mainly extend the results on self-expanders which we obtained in \cite{ancari2020volum} to $λ$-self-expanders. We prove some results that characterize the hyperplanes, spheres and cylinders as $λ$-self-expanders. We also discuss the area growths and the finiteness of the weighted areas under the control of the growth of the mean curvature.
