Regularity of area minimizing currents mod p - De Lellis, Camillo; Hirsch, Jonas; Marchese, Andrea; Stuvard, Salvatore (Geometric and functional analysis, 2020)
We establish a first general partial regularity theorem for area minimizing currents mod ( p ) , for every p , in any dimension and codimension. More precisely, we prove that the Hausdorff dimension of the interior singular set of an m -dimensional area minimizing current mod ( p ) cannot be larger than m - 1 . Additionally, we show that, when p is odd, the interior singular set is ( m - 1 ) -rectifiable with locally finite ( m - 1 ) -dimensional measure.