Asymptotic expansion and optimal symmetry of minimal gradient graph equations in dimension 2

TL;DR

This paper investigates the asymptotic behavior and symmetry of zero mean curvature equations in two dimensions, including Monge-Ampère and special Lagrangian equations, refining existing classifications and understanding of minimal gradient graphs.

Contribution

It provides a detailed asymptotic expansion at infinity and characterizes symmetry for minimal gradient graphs, extending classification results for Monge-Ampère equations in dimension two.

Findings

Refined asymptotic expansion at infinity for zero mean curvature equations

Established symmetry properties of minimal gradient graphs in 2D

Extended classification results for Monge-Ampère equations

Abstract

In this paper, we study asymptotic expansion at infinity and symmetry of zero mean curvature equations of gradient graph in dimension 2, which include the Monge--Amp\`ere equation, inverse harmonic Hessian equation and the special Lagrangian equation. This refines the research of asymptotic behavior, gives the precise gap between exterior minimal gradient graph and the entire case, and extends the classification results of Monge--Amp\`ere equations.