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arXiv · 1202.1053

Complete self-shrinkers of the mean curvature flow

Qing-Ming Cheng·Yejuan Peng
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Abstract

It is our purpose to study complete self-shrinkers in Euclidean space. By introducing a generalized maximum principle for $\mathcal{L}$-operator, we give estimates on supremum and infimum of the squared norm of the second fundamental form of self-shrinkers without assumption on \emph{polynomial volume growth}, which is assumed in Cao and Li. Thus, we can obtain the rigidity theorems on complete self-shrinkers without assumption on \emph{polynomial volume growth}. For complete proper self-shrinkers of dimension 2 and 3, we give a classification of them under assumption of constant squared norm of the second fundamental form.

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Qing-Ming Cheng, Yejuan Peng. 2012-02-06. Complete self-shrinkers of the mean curvature flow. https://arxiv.org/abs/1202.1053

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