Rigidity of limit sets for nonplanar geometrically finite Kleinian groups of the second kind

Abstract

We consider the relation between geometrically finite groups and their limit sets in infinite-dimensional hyperbolic space. Specifically, we show that a rigidity theorem of Susskind and Swarup (Am J Math 114(2):233–250, 1992) generalizes to infinite dimensions, while a stronger rigidity theorem of Yang and Jiang (Bull Aust Math Soc 82(1):1–9, 2010) does not.