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A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\)

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Abstract

In this paper we study the complete Lagrangian translators in the complex 2-plane \(\mathbb C^2\). As the result, we obtain a uniqueness theorem showing that the plane is the only complete Lagrangian translator in \(\mathbb C^2\) with constant square norm of the second fundamental form. On the basis of this, we can prove a more general classification theorem for Lagrangian \(\xi \)-translators in \({\mathbb C}^2\). The same idea is also used to give a similar classification of Lagrangian \(\xi \)-surfaces in \({\mathbb C}^2\).

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan Normal University, Xinxiang, 453007, People’s Republic of China

    Xingxiao Li, Yangyang Liu & Ruina Qiao

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  1. Xingxiao Li
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  2. Yangyang Liu
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  3. Ruina Qiao
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Correspondence to Xingxiao Li.

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Research supported by Foundation of Natural Sciences of China (Nos. 11671121, 11871197 and No 11971153).

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Li, X., Liu, Y. & Qiao, R. A uniqueness theorem of complete Lagrangian translator in \(\mathbb C^2\). manuscripta math. 164, 251–265 (2021). https://doi.org/10.1007/s00229-020-01185-3

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