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Jun 12 at 19:35 vote accept Roman
Jun 11 at 22:50 history edited Moishe Kohan CC BY-SA 4.0
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Jun 11 at 22:35 history edited Moishe Kohan CC BY-SA 4.0
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Jun 11 at 21:32 comment added Moishe Kohan Yes, it is unique in this case, but I do not know an easy proof. It is probably in the literature.
Jun 11 at 21:27 comment added Moishe Kohan I am unsure. My guess is that in the GH (strictly convex) case the domain is unique. It is so if $n=3$. @Roman
Jun 11 at 20:59 comment added Roman Indeed, thanks! Do you know, what is about non-equivalent domains? (By a projective transformation.) And about Gromov hyperbolic subgroups?
Jun 11 at 20:49 history answered Moishe Kohan CC BY-SA 4.0