The non-Stein characterization for critical exponent two

Let $\Gamma<\operatorname{Aut}(\mathbf B^n)$ be a convex-cocompact, torsion-free subgroup, and let $M_\Gamma=\mathbf B^n/\Gamma$. Suppose that $\delta(\Gamma)=2$. The non-Stein characterization conjecture. The manifold $M_\Gamma$ is non-Stein if and only if $\Gamma$ is a complex Fuchsian subgroup. Complex Fuchsian subgroups give non-Stein quotients because their convex cores are complex curves; the conjecture asserts that these are the only non-Stein examples at critical exponent two.