Examples of topological sphere $\lambda$-self-expander

Abstract

A $\lambda$-self-expander $F:M^n\to {\mathbb{R}}^{n+1}$ is the solution of the isoperimetric problem of weight $e^{\frac{|x{|}^2}{4}}$. In this paper, for sufficiently large $\lambda$, we construct an immersed non-embedded spherical $\lambda$-self-expander in ${\mathbb{R}}^{n+1}$ with the mean curvature $H>0$. Moreover, we obtain the explicit solution for $n=2$.

arXiv comment32 pages Version 2: Minor correction, fixed misspelling of Florian Johne's surname in the text and references