Complete lagrangian self-expanders in $\mathbb C^{2}$

TL;DR

This paper classifies 2-dimensional complete Lagrangian self-expanders in complex 2-space with constant squared second fundamental form, advancing understanding of their geometric structure.

Contribution

It provides a classification theorem for such self-expanders, a specific geometric condition not previously fully characterized.

Findings

Classification of 2D complete Lagrangian self-expanders with constant squared second fundamental form

New geometric insights into the structure of these self-expanders

Extension of previous results in Lagrangian mean curvature flow

Abstract

In this paper, we obtain a classification theorem of $2$-dimensional complete Lagrangian self-expanders with constant squared norm of the second fundamental form in $\mathbb C^{2}$.