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

TL;DR

This paper classifies all 2-dimensional complete Lagrangian self-shrinkers in four-dimensional Euclidean space with constant squared second fundamental form, advancing understanding of mean curvature flow singularities.

Contribution

It provides a complete classification of 2D Lagrangian self-shrinkers in R^4 with constant second fundamental form, a new result in geometric analysis.

Findings

Classification of 2D Lagrangian self-shrinkers in R^4

Identification of conditions for constant squared second fundamental form

Advancement in understanding mean curvature flow singularities

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.