We study the spherical droplet problem in 3D Landau–de Gennes theory with finite temperature. By rigorously constructing biaxial–ring solutions and split–core–segment solutions, we theoretically confirm numerical results of Gartland–Mkaddem [15]. The structures disclinations are also addressed.

Let W?C[x1,?,xN] be an invertible polynomial with isolated singularity at origin, and let G?SLN?(C?)N a finite diagonal special linear symmetry group of W. In this paper, we use the category MFG(W) G-equivariant matrix factorizations its associated VSHS to construct version Saito's theory primitive forms. We prove there exists canonical categorical form characterized by GWmax-equivariance. Conj...