Removability of singular sets of harmonic maps

It is proved that a harmonic map with small energy and the monotonicity property is smooth if its singular set is rectifiable and has a finite uniform density; moreover, the monotonicity property holds if the singular set has a lower dimension or its gradient has higher integrability. This work generalizes the results in CL, DF, LG12], which were proved under the assumption that the singular sets are isolated points or smooth submanifolds.