  In the Landau-de Gennes theoretical framework of a $Q -tensor description of
nematic liquid crystals, we consider a radial hedgehog defect with strong
anchoring conditions in a ball $B \subset \mathbb{R}^3$ . We show that the
scalar order parameter is monotonic, and we prove uniqueness of the minimizing
hedgehog below the spinodal temperature $T^\ast$ .
