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arXiv · 1405.4230

Self-Shrinkers With Second Fundamental Form of Constant Length

Qiang Guang
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Abstract

In this note, we give a new and simple proof of a result in {\cite{DX1}} which states that any smooth complete self-shrinker in $\mathbb{R}^3$ with second fundamental form of constant length must be a generalized cylinder $\mathbb{S}^k \times \mathbb{R}^{2-k}$ for some $k\leq2$. Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions.

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Qiang Guang. 2014-05-16. Self-Shrinkers With Second Fundamental Form of Constant Length. https://doi.org/10.1017/s0004972717000053

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