A characterization of the standard tori in \(\mathbb{C}^2\) as compact Lagrangian \(\xi \)-submanifolds

DOI10.1007/s11401-022-0336-3zbMath1504.53090OpenAlexW4313179358MaRDI QIDQ2094312

Ruiwei Xu, Xing Xiao Li

Publication date: 28 October 2022

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-022-0336-3

zbMATH Keywords

second fundamental formmean curvature vector\(\xi\)-submanifoldstandard tori

Mathematics Subject Classification ID

Other complex differential geometry (53C56) Lagrangian submanifolds; Maslov index (53D12) Local submanifolds (53B25)

Cites Work

• Unnamed Item
• Generic mean curvature flow. I: Generic singularities
• Rigidity theorems of \(\lambda\)-hypersurfaces
• Classification and rigidity of self-shrinkers in the mean curvature flow
• Variational characterizations of \(\xi\)-submanifolds in the Eulicdean space \(\mathbb{R}^{m+p}\)
• Asymptotic behavior for singularities of the mean curvature flow
• A gap theorem for self-shrinkers of the mean curvature flow in arbitrary codimension
• New characterizations of the Clifford torus as a Lagrangian self-shrinker
• Construction of Lagrangian self-similar solutions to the mean curvature flow in \(\mathbb C^n\)
• A rigidity theorem of \(\xi \)-submanifolds in \({\mathbb {C}}^{2}\)
• The Clifford Torus as a Self-Shrinker for the Lagrangian Mean Curvature Flow
• Gap and rigidity theorems of 𝜆-hypersurfaces
• Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in the complex Euclidean plane

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