Year: 2022
Type: preprint
Abstract: $λ$-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.
Source: arXiv (Cornell University)
Authors: Ancari, Saul, Cheng, Xu
Institution: Universidade Federal Fluminense
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4292957494