Closed Lagrangian self-shrinkers in ℝ⁴ symmetric with respect to a hyperplane

2020/07/14 by Jae‐Hoon Lee, Lee, Jaehoon
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2007.06839

Abstract

In this paper, we prove that the closed Lagrangian self-shrinkers in ℝ⁴ which are symmetric with respect to a hyperplane are given by the products of Abresch-Langer curves. As a corollary, we obtain a new geometric characterization of the Clifford torus as the unique embedded closed Lagrangian self-shrinker symmetric with respect to a hyperplane in ℝ⁴.

Citations

• Embedded minimal tori in S3 and the Lawson conjecture

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• Geometry of Lagrangian self-shrinking tori and applications to the Piecewise Lagrangian Mean Curvature Flow