Uniqueness of Lagrangian Self-Expanders

TL;DR

This paper proves local and global uniqueness results for certain Lagrangian self-expanders in complex Euclidean space, depending on the dimension, by analyzing their asymptotic behavior to intersecting planes.

Contribution

It establishes the local uniqueness of zero-Maslov class Lagrangian self-expanders in higher dimensions and their global uniqueness in the two-dimensional case.

Findings

Local uniqueness for n>2

Global uniqueness for n=2

Asymptotic to intersecting planes

Abstract

We show that zero-Maslov class Lagrangian self-expanders in C^n which are asymptotic to a pair of planes intersecting transversely are locally unique if n>2 and unique if n=2.