Minimal surface systems, maximal surface systems, and special Lagrangian equations

TL;DR

This paper extends classical results on minimal and maximal surface systems, constructs explicit special Lagrangian graphs, and generalizes Calabi's correspondence, advancing understanding of geometric PDEs in higher codimension.

Contribution

It generalizes Osserman's lemma, constructs explicit special Lagrangian Scherk graphs, and extends Calabi's correspondence to higher codimension minimal and maximal graphs.

Findings

Extended Osserman's lemma for higher codimension

Constructed explicit special Lagrangian Scherk graphs

Generalized Calabi's correspondence between minimal and maximal graphs

Abstract

We extend Osserman's lemma on the generalized Gauss map of two-dimensional minimal graphs of higher codimension, construct a Jenkins-Serrin type special Lagrangian Scherk graph explicitly, and generalize Calabi's correspondence between minimal graphs and maximal graphs.