Chengbo Yue's gap conjecture for convex-cocompact subgroups

Let $G=\operatorname{Aut}(\mathbf B^n)$, and let $\Gamma<G$ be a convex-cocompact torsion-free subgroup. Let $\delta_\Gamma$ denote its critical exponent. Chengbo Yue's gap conjecture. Either $\Gamma$ is a uniform lattice in $G$, in which case $\delta_\Gamma=2n$, or $\delta_\Gamma\le 2n-1$. The conjecture concerns a proposed gap below the lattice value for convex-cocompact subgroups; the source records it as open and notes that related conjectures fail already in dimension $n=2$.