Generic uniqueness for the Plateau problem

Given a complete Riemannian manifold $\mathcal{M}\subset\mathbb{R}^d$ which is a Lipschitz neighbourhood retract of dimension $m+n$, of class $C^{h,\beta}$ and an oriented, closed submanifold $\Gamma \subset \mathcal M$ of dimension $m-1$, which is a boundary in integral homology, we construct a complete metric space $\mathcal{B}$ of $C^{h,\alpha}$-perturbations of $\Gamma$ inside $\mathcal{M}$, with $\alpha