New characterizations of the Clifford torus as a Lagrangian self-shrinker

2015/05/21 by Li, Haizhong, Wang, Xianfeng · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.05593

Abstract

In this paper, we obtain several new characterizations of the Clifford torus as a Lagrangian self-shrinker. We first show that the Clifford torus \mathbbS¹(1)×\mathbbS¹(1) is the unique compact orientable Lagrangian self-shrinker in ℂ² with |A|²≤ 2, which gives an affirmative answer to Castro-Lerma's conjecture. We also prove that the Clifford torus is the unique compact orientable embedded Lagrangian self-shrinker with nonnegative or nonpositive Gauss curvature in ℂ².

Cited by

• Relative Liouville Rigidity for Lagrangian Self-Similar Submanifolds with Legendrian Boundary
• Rigidity and Classification of Legendrian Self-Shrinkers

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