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The second gap on complete self-shrinkers

Authors :
Cheng, Qing-Ming
Wei, Guoxin
Yano, Wataru
Publication Year :
2021

Abstract

In this paper, we study complete self-shrinkers in Euclidean space and prove that an $n$-dimensional complete self-shrinker in Euclidean space $\mathbb{R}^{n+1}$ is isometric to either $\mathbb{R}^{n}$, $S^{n}(\sqrt{n})$, or $S^k (\sqrt{k})\times\mathbb{R}^{n-k}$, $1\leq k\leq n-1$, if the squared norm $S$ of the second fundamental form, $f_3$ are constant and $S$ satisfies $S<1.83379$. We should remark that the condition of polynomial volume growth is not assumed.

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2104.14059
Document Type :
Working Paper