Minimizing fractional harmonic maps on the real line in the supercritical regime

This article addresses the regularity issue for minimizing fractional harmonic maps of order $s\in (0,1\mathrm{/}2)$ from an interval into a smooth manifold. H"older continuity away from a locally finite set is established for a general target. If the target is the standard sphere, then H"older continuity holds everywhere.