Complex visibility characterization for bounded convex domains

Let $\Omega\subset\mathbb C^N$ be a bounded convex domain. It is complex visible if for every distinct $p,q\in\partial\Omega$ there exist a compact set $K\Subset\Omega$ and open neighborhoods $U$ of $p$ and $V$ of $q$ such that every sequence of complex geodesics joining sequences converging to $p$ and $q$ intersects $K$ for all sufficiently large indices. Complex visibility conjecture. Then $\Omega$ is visible if and only if it is complex visible. Visibility already implies complex visibility, so the open direction is the converse.