A one-sentence proof of the Bernstein type theorem for special Lagrangian equation in two dimensions

TL;DR

This paper demonstrates the equivalence between Jörgens' Theorem for the unimodular Hessian equation and Fu's Theorem for the special Lagrangian equation in two dimensions, providing a simplified proof of Bernstein type results.

Contribution

It establishes a direct equivalence between two classical theorems, offering a new, concise proof of the Bernstein type theorem for the special Lagrangian equation in two dimensions.

Findings

Proves the equivalence of Jörgens' and Fu's theorems in 2D.

Provides a simplified proof of the Bernstein type theorem.

Highlights the connection between Hessian and special Lagrangian equations.

Abstract

The aim of this expository article is to reveal the equivalence of J\"orgens' Theorem on the two dimensional unimodular Hessian equation and Fu's Theorem on the two dimensional special Lagrangian equation.