A partial regularity result of harmonic maps from manifolds with bounded measurable Riemannian metrics (Q1922778)

Suppose \(M\) is an \(n\)-dimensional differentiable manifold with Riemannian metric tensor \(g\). If the components \(g_{ij}\) of \(g\) in each coordinate \(\text{chart}D\) belong merely to \(L^\infty(D,R)\), then \(g\) is called a bounded measurable Riemannian metric. In this paper, the author proves partial regularity results of energy minimizing maps from manifolds with bounded measurable Riemannian metrics to a smooth compact Riemannian manifold. The \((n-2)\)-dimensional Hausdorff measure of the singular set of the map is also obtained.