Zero-homogeneous and $O(2)$-equivariant critical points of the Oseen-Frank energy with multiple Frank constants

We give an existence and classification result for zero-homogeneous and $O(2)$-equivariant critical points of the Oseen-Frank energy with multiple Frank constants. These critical points carry a topological defect of degree one and are minimizing with respect to $O(2)$-equivariant perturbations supported away from the axis of symmetry.