Nguyen–Stancu–Wei fundamental gap conjecture for horoconvex hyperbolic domains

Let $N$ be the dimension, let $\mathbb H^N$ be hyperbolic $N$-space, and let $\Omega\subset\mathbb H^N$ be a horoconvex domain. Write $\Gamma(\Omega)$ for its fundamental gap, namely the difference between the first two Dirichlet eigenvalues of the Laplacian on $\Omega$. For a prescribed diameter bound $D>0$, Nguyen–Stancu–Wei's conjecture. There \exists a constant $c(N,D)>0$ such that every horoconvex domain $\Omega\subset\mathbb H^N$ of diameter at most $D$ satisfies

$$\Gamma(\Omega)\geq c(N,D).$$

The conjecture asserts a uniform positive lower bound for the fundamental gap under horoconvexity, in contrast with the arbitrarily small gaps possible for merely convex hyperbolic domains. The supplied source does not indicate whether this conjecture has been resolved.