Defects of liquid crystals with variable degree of orientation

TL;DR

This paper analyzes the structure of defects in liquid crystals with variable orientation, showing that the defect set comprises isolated points and finitely many H"older continuous curves with limited crossings.

Contribution

It proves the local structure of the defect set for minimizers of the modified Ericksen energy, revealing geometric properties of defects in liquid crystals with variable orientation.

Findings

Defect set consists of isolated points and H"older continuous curves.

Finitely many crossings in the defect curves.

Local structure characterized for minimizers of the energy.

Abstract

We prove that the zero set of a minimizer of the modified Ericksen energy for nematic liquid crystals with variable degree of orientation consists locally of isolated points and a finite union of H\"older continuous curves with only finitely many crossings.