Classification of Lagrangian translators and Lagrangian self-expanders in $\mathbb{C}^{2}$

Zhi Li; Guoxin Wei

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arXiv · 2405.14086

Classification of Lagrangian translators and Lagrangian self-expanders in $\mathbb{C}^{2}$

Zhi Li·Guoxin Wei

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Abstract

In this paper, we obtain several classification results of $2$-dimensional complete Lagrangian translators and lagrangian self-expanders with constant squared norm $|\vec{H}|^{2}$ of the mean curvature vector in $\mathbb{C}^{2}$ by using a new Omori-Yau type maximum principle which was proved by Chen and Qiu \cite{CQ}. The same idea is also used to give a similar result of Lagrangian $\xi$-translators in $\mathbb{C}^{2}$.

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BibTeX RIS

Zhi Li, Guoxin Wei. 2024-05-23. Classification of Lagrangian translators and Lagrangian self-expanders in $\mathbb{C}^{2}$. https://arxiv.org/abs/2405.14086

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