The volume of a unit vector field in 2 dimensions via calibrations

TL;DR

This paper applies calibration theory to derive the equation governing minimal volume vector fields on Riemann surfaces, providing a geometric approach to understanding such fields.

Contribution

It introduces a calibration-based method to characterize minimal volume vector fields on Riemann surfaces, linking geometric analysis with variational principles.

Findings

Derived explicit equations for minimal volume vector fields

Connected calibration theory with geometric analysis on Riemann surfaces

Provided a new framework for studying minimal vector fields

Abstract

We use the theory of calibrations to write the equation of a minimal volume vector field on a given Riemann surface.