Closed Lagrangian self-shrinkers in $\mathbb{R}^4$ symmetric with respect to a hyperplane

Jaehoon Lee

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arXiv · 2007.06839

Closed Lagrangian self-shrinkers in $\mathbb{R}^4$ symmetric with respect to a hyperplane

Jaehoon Lee

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Abstract

In this paper, we prove that the closed Lagrangian self-shrinkers in $\mathbb{R}^4$ 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 $\mathbb{R}^4$.

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Jaehoon Lee. 2020-07-14. Closed Lagrangian self-shrinkers in $\mathbb{R}^4$ symmetric with respect to a hyperplane. https://arxiv.org/abs/2007.06839

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