Interior regularity of area minimizing currents within a C2,α-submanifold

Given an area-minimizing integral m-current in Σ, we prove that the Hausdorff dimension of the interior singular set of T cannot exceed $m-2$, provided that Σ is an embedded (m+n̄)-submanifold of Rᵐ⁺ⁿ of class C2,α, where α>0. This result establishes the complete counterpart, in the arbitrary codimension setting, of the interior regularity theory for area-minimizing integral hypercurrents within a Riemannian manifold of class C2,α.