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arXiv · 2412.01162

The rigidity theorem for complete Lagrangian self-shrinkers

Zhi Li·Ruixin Wang·Guoxin Wei
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Abstract

In this paper, we obtain a rigidity result of $2$-dimensional complete lagrangian self-shrinkers with constant squared norm $|\vec{H}|^{2}$ of the mean curvature vector in the Euclidean space $\mathbb{R}^{4}$. The same idea is also used to give a similar result of Lagrangian $\xi$-submanifolds in $\mathbb{R}^{4}$.

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Zhi Li, Ruixin Wang, Guoxin Wei. 2024-12-02. The rigidity theorem for complete Lagrangian self-shrinkers. https://arxiv.org/abs/2412.01162

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