Approaching complex geodesics in Gromov hyperbolic bounded convex domains

Determine whether every bounded convex domain D in C^d whose Kobayashi metric space (D, k_D) is Gromov hyperbolic has the approaching complex geodesics property, namely that any two asymptotic complex geodesic rays in D are strongly asymptotic.

Background

The authors introduce a weaker condition than approaching geodesics for convex domains: approaching complex geodesics, which requires strong asymptoticity only for rays contained in complex geodesics. They prove this holds for bounded convex finite type domains using McNeal scaling, which already implies equivalence of the horofunction and Gromov compactifications.

They explicitly pose whether this weaker property extends to all bounded convex domains that are Gromov hyperbolic with respect to the Kobayashi metric.