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 subset of R-3. We show that the scalar order parameter is monotonic, and we prove uniqueness of the minimizing hedgehog below the spinodal temperature T*. (C) 2012 Elsevier Inc. All rights reserved.