Improved partial regularity for manifold-constrained minimisers of subquadratic energies

Abstract

We consider minimising $p$-harmonic maps from three-dimensional domains to the real projective plane, for $1<p<2$. 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.