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The second gap on complete self-shrinkers
- 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.
- Subjects :
- Mathematics - Differential Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2104.14059
- Document Type :
- Working Paper