Some rigidity properties for $\lambda$-self-expanders

Saul Ancari; Xu Cheng

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arXiv · 2208.09608

Some rigidity properties for $\lambda$-self-expanders

Saul Ancari·Xu Cheng

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Abstract

$\lambda$-self-expanders $\Sigma$ 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 $\lambda$-self-expanders. We prove some results that characterize the hyperplanes, spheres and cylinders as $\lambda$-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.

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Saul Ancari, Xu Cheng. 2022-08-20. Some rigidity properties for $\lambda$-self-expanders. https://arxiv.org/abs/2208.09608

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