SELF-SHRINKERS WITH SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH

QIANG GUANG
2017 Bulletin of the Australian Mathematical Society  
We give a new and simple proof of a result of Ding and Xin, which states that any smooth complete self-shrinker in $\mathbb{R}^{3}$ with the second fundamental form of constant length must be a generalised cylinder $\mathbb{S}^{k}\times \mathbb{R}^{2-k}$ for some $k\leq 2$ . Moreover, we prove a gap theorem for smooth self-shrinkers in all dimensions.
doi:10.1017/s0004972717000053 fatcat:vizuel4xw5aktiojncebjyqktm