Some rigidity properties for $λ$-self-expanders

$λ$-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.

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