Abstract We study fine structural properties related to the interior regularity of 𝑚-dimensional area-minimizing currents mod (q) mod (q) in arbitrary codimension. We show (i) the set of points where at least one tangent cone is translation invariant along m − 1 m-1 directions is locally a connected C 1, β C^1, submanifold, and moreover such points have unique tangent cones; (ii) the remaining part of the singular set is countably (m − 2) (m-2) -rectifiable, with a unique flat tangent cone (possibly with multiplicity) at H m − 2 H^m-2 -a. e. flat singular point. These results are consequences of fine excess decay theorems as well as almost monotonicity of a universal frequency function.
Lellis et al. (Thu,) studied this question.