A solution to the Bernstein problem in the three-dimensional Heisenberg group via loop groups

TL;DR

This paper offers a concise alternative proof for the Bernstein problem in the 3D Heisenberg group using loop group techniques, contributing to geometric analysis in sub-Riemannian geometry.

Contribution

It introduces a novel proof method for the Bernstein problem in ${ m Nil}_3$ leveraging loop group techniques, differing from traditional approaches.

Findings

Provides an alternative proof for the Bernstein problem in ${ m Nil}_3$

Utilizes loop group methods in sub-Riemannian geometry

Simplifies understanding of minimal surfaces in Heisenberg groups

Abstract

In this note we present a short alternative proof for the Bernstein problem in the three-dimensional Heisenberg group ${\rm Nil}_3$ by using the loop group technique.