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In [AHL] Hardt, Lin and the author proved that the defect set of minimizersof the modified Ericksen energy for nematic liquid crystals consists locally ofa finite union of isolated points and H\"older continuous curves with finitelymany crossings. In this article, we show that each H\"older continuous curve inthe defect set is of finite length. Hence, the defect set is locallyrectifiable. For the most part, the proof follows the work of De Lellis,Marchese, Spadaro and Valtorta [DLMSV] on harmonic $\mathcal{Q}$-valued mapsclosely. The blow-up analysis in [AHL] allows us to simplify the coveringarguments in [DLMSV] and locally estimate the length of line defects in ageometric fashion.

Rectifiability of line defects in liquid crystals with variable degree of orientation