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SELF-SHRINKERS WITH SECOND FUNDAMENTAL FORM OF CONSTANT LENGTH
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 96 / Issue 2 / October 2017
- Published online by Cambridge University Press:
- 02 March 2017, pp. 326-332
- Print publication:
- October 2017
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- Article
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- You have access
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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.
