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Complete Lagrangian self-shrinkers in \({\mathbf {R}}^4\)

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The purpose of this paper is to study complete self-shrinkers of mean curvature flow in Euclidean spaces. In the paper, we give a complete classification for 2-dimensional complete Lagrangian self-shrinkers in Euclidean space \({\mathbb {R}}^4\) with constant squared norm of the second fundamental form.

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Acknowledgements

The authors would like to thank the referee for his/her valuable comments and suggestions.

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Correspondence to Guoxin Wei.

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Dedicated to Professor Yuan-Long Xin for his 75th birthday.

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The Qing-Ming Cheng was partially supported by JSPS Grant-in-Aid for Scientific Research (B): No. 16H03937. The Guoxin Wei was partly supported by NSFC Grant Nos. 12171164, 11771154, Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme (2018), Guangdong Natural Science Foundation Grant No. 2019A1515011451.

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Cheng, QM., Hori, H. & Wei, G. Complete Lagrangian self-shrinkers in \({\mathbf {R}}^4\). Math. Z. 301, 3417–3468 (2022). https://doi.org/10.1007/s00209-022-03027-2

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