Existence of torsion-free $G_2$-structures on resolutions of $G_2$-orbifolds using weighted Holder norms

An alternative proof of the existence of torsion-free $G_2$-structures on resolutions of $G_2$-orbifolds considered in arXiv:1707.09325 is given. The proof uses weighted Holder norms which are adapted to the geometry of the manifold. This leads to better control of the torsion-free $G_2$-structure and a simplification over the original proof.