By a 1990 paper of Michael Anderson, the following is true:

**Theorem.** *Let the metric space* $(X,d,p)$ *be a pointed Gromov-Hausdorff limit of a sequence of complete pointed Riemannian manifolds* $(M_i,g_i, p_i)$ *satisfying the uniform bounds*

*[*$|Ric(g_i)|\leq \lambda$**two-sided Ricci**]*[*$\int\limits_M |Rm(g_i)|^{n/2} \leq \Lambda$**$L^{n/2}$ norm of curvature**]*[*for some $r_0$, $\inf\limits_{q\in M_i, r\leq r_0} \ vol(B(q,r))/r^n\geq v$.**non-collapsing**]

*Then $(X,d,p)$ is (topologically) a smooth orbifold, whose singularities are of the form $\mathbb{R}^n/\Gamma$ for some finite $\Gamma\subseteq SO(n)$.*

I'm trying to get a sense of how sharp this statement is. Here's a possible converse.

**Question.** *Suppose I have a spherical space form $S^{n-1}/\Gamma$, and a $n$-manifold $M$ with boundary $\partial M = S^{n-1}/\Gamma$. Can I construct a sequence of complete Riemannian metrics on $M$'s interior, all satisfying the bounds above, such that some pointed Gromov-Hausdorff limit is homeomorphic to $\mathbb{R}^n/\Gamma$?*

A few remarks on what I know: I am aware of some standard constructions for particular $\Gamma$, such as the ALE hyperkähler metrics for $\Gamma\subseteq SU(2)$. However, I don't know any good general ways to construct a family of metrics satisfying two-sided Ricci bounds.