“…The regularity theory for extrinsic 1 2 -harmonic maps has been extended to a range of fractional powers for maps into general target manifolds N by Da Lio et al [6,7,9,35,36] etc, as well as Millot and Sire [25] for the power 1 2 . Millot-Sire and Yu have also considered the regularity of extrinsic minimising fractional harmonic maps defined on the real line for powers in (0, 1 2 ) [26]. The methods Da Lio, Rivière and Schikorra used to obtain regularity take advantage of compensation phenomena, namely higher than expected regularity which can be derived from the Euler-Lagrange equations for the energies they considered.…”