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<p<2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p<2$$\end{document}. 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.