F. H. Lin's Lipschitz regularity conjecture for energy-minimizing maps on Alexandrov spaces

Let $\Omega$ be a bounded open domain in an $n$-dimensional Alexandrov space with curvature bounded from below by $k$, and let $N$ be a compact smooth Riemannian manifold. Suppose $u$ is an energy-minimizing map, so that Theorem 1.1 gives local Hölder continuity in $\Omega$ away from a relatively closed subset of Hausdorff dimension at most $n-3$. F. H. Lin's conjecture. The Hölder continuity can be improved to Lipschitz continuity in Theorem 1.1. This conjecture asks whether the partial Hölder regularity of energy-minimizing maps from Alexandrov spaces can be strengthened to partial Lipschitz regularity; the supplied source does not indicate that it has been resolved.