On the Jacobian of minimal graphs in R^4

TL;DR

This paper characterizes complex analytic curves among two-dimensional minimal graphs in four-dimensional space using the Jacobian, providing insights into the geometric structure of such minimal surfaces.

Contribution

It introduces a novel characterization criterion for complex analytic curves within minimal graphs in R^4 based on the Jacobian.

Findings

Complex analytic curves are distinguished by specific Jacobian properties.

The characterization helps identify complex structures in minimal surfaces.

The results deepen understanding of minimal surface geometry in higher dimensions.

Abstract

We provide a characterization for complex analytic curves among two-dimensional minimal graphs in $\mathbb{R}^{4}$ via the Jacobian