Improved Partial Regularity for Manifold-Constrained Minimisers of Subquadratic Energies

We consider minimising p-harmonic maps from three-dimensional domains to the real projective plane, for 1<<2. These maps arise as least-energy configurations in variational models for nematic liquid crystals. We show that the singular set of such a map decomposes into a 1-dimensional set, which can be physically interpreted as a non-orientable line defect, and a locally finite set, i.e. a collection of point defects.