Some properties of the nematic radial hedgehog in the Landau–de Gennes theory

We consider, in the Landau–de Gennes theoretical framework of a Q -tensor description of nematic liquid crystals, a radial hedgehog defect with strong anchoring conditions in a ball B ⊂ R 3 . We show that the scalar order parameter is monotonic, and we prove uniqueness of the minimizing hedgehog below the spinodal temperature T ∗ .