Year: 2026
Type: preprint
Abstract: Let $X: M^{n}\to \mathbb{R}^{n+1}$ be a complete self-shrinker with constant squared norm of the second fundamental form $S$. In this paper, we prove that if $S\leq \frac{10}{7}$, then $S=1$ or $S=0$, and the self-shrinker is isometric to either a round sphere $\mathbb{S}^n(\sqrt{n})$ with the center at the origin, or a cylinder $\mathbb{S}^k(\sqrt{k})\times \mathbb{R}^{n-k},~~1\leq k\leq n-1$, or a plane through the origin.
Source: arXiv (Cornell University)
Authors: Cheng, Pengpeng, Li, Tongzhu
Institution: Beijing Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2131439191
OpenAlex ID: W7214598453