Rectifiability of the singular set of energy minimizing maps (Q1343744)

Let \(\Omega\subset \mathbb{R}^ n\) be a domain, \(N\) be a compact real- analytic Riemannian manifold and \(u\) be an energy minimizing map of \(\Omega\) into \(N\). The main results of this paper are: 1) For each closed ball \(B\subset \Omega\), the set \(B\cap\text{sing }u\) is the union of a finite pairwise disjoint collection of locally \((n- 3)\)-rectifiable locally compact subsets. 2) For each integer \(m\in \{0,\dots, n- 3\}\), let \(S^{(m)}\) be the set of points \(z\in \text{sing }u\) such that \(\dim\text{sing }\varphi\leq m\) for every tangent map \(\varphi\) of \(u\) and \(z\). Then \(S^{(m)}\) is countably \(m\)-rectifiable, \(m= 0,\dots, n- 3\).