A partial regularity result for harmonic maps into a Finsler manifold (Q1566345)

As a model case the author considers mappings \(u\) from a domain \(\Omega\) in \(\mathbb{R}^m\) into the space \(N= (\mathbb{R}^n, F)\), where \(F\) denotes a smooth Finsler structure. Since there is a natural definition of the Dirichlet energy \(E(u,\Omega)\), it makes sense to study the minimization problem \(E(\cdot,\Omega)\to\min\) in the Sobolev class \(W^{1,2}_f(\Omega, N)\) for a given boundary function \(f:\partial\Omega\to N\). The author proves that the \((m-2-\varepsilon)\)-dimensional Hausdorff measure of the singular set of every energy minimizing map is \(0\) for some \(\varepsilon\in (0,1)\), when \(m= 3,4\).