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

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 ${\mathbb{R}}^4$.

12 pages

References in corpus (1)

• The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow