2-dimensional complete self-shrinkers in $\mathbf{R}^3$

Qing-Ming Cheng; Shiho Ogata

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arXiv · 1504.02225

2-dimensional complete self-shrinkers in $\mathbf{R}^3$

Qing-Ming Cheng·Shiho Ogata

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Abstract

It is our purpose to study complete self-shrinkers in Euclidean space. First of all, we show some examples of complete self-shrinkers without polynomial volume growth. By making use of the generalized maximum principle for $\mathcal{L}$-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in $\mathbb R^3$. In \cite{DX2}, Ding and Xin have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.

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Qing-Ming Cheng, Shiho Ogata. 2015-04-09. 2-dimensional complete self-shrinkers in $\mathbf{R}^3$. https://arxiv.org/abs/1504.02225

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