In this paper, we investigate the structure of local minimizers for the isotropic–nematic interface based on the Landau-de Gennes energy. In the absence of the anisotropic energy, the uniaxial solution is the only local minimizer in 1-D. In 3-D, we propose a De Giorgi’s type conjecture and give an affirmative answer under a mild assumption. In the presence of the anisotropic energy with L2 > −1 and homeotropic anchoring, the uniaxial solution is also the only local minimizer in a class of diagonal form in 1-D.