Semi-calibrated 2-currents are pseudo holomorphic, with applications

TL;DR

This paper proves that semi-calibrations of degree 2 induce local almost complex structures and explores applications in the regularity theory of semi-calibrated 2-currents.

Contribution

It establishes a new link between semi-calibrations and almost complex structures, advancing understanding in geometric measure theory.

Findings

Semi-calibrations of degree 2 are locally induced by smooth almost complex structures.

Applications improve regularity results for semi-calibrated 2-currents.

Abstract

We show that any semi-calibration of degree 2 is locally induced by a smooth almost complex structure. We provide some applications of this result in the regularity theory for semi-calibrated 2-currents