Complete Lagrangian self-shrinkers in ${\mathbf{R}}^4$

Abstract

The purpose of this paper is to study complete self-shrinkers of mean curvature flow in Euclidean spaces. In the paper, we give a complete classification for 2-dimensional complete Lagrangian self-shrinkers in Euclidean space ${\mathbb{R}}^4$ with constant squared norm of the second fundamental form.

53 pages