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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.
