Admissible Limit Sets of Discrete Groups On Symmetric Spaces of Rank One

TL;DRAbstract

In recent years it has become increasingly clear that a number of important results about limit sets of discrete groups acting on real hyperbolic space H R n remain true also for the complex, quarternionic, and two- dimensional octonionic spaces, . for all non-compact Riemannian symmetric spaces of rank one [Ka], [C], [CI], [BJ]. There are two essential elements in these generalizations. One is the description of the “non- tangential” or “conical” boundary approach domains of the Poincaré model of H R n as tubes of constant diameter around geodesic rays: We call these the admissible domains. The other is the intrinsic, in general non-isotropic, metric of the boundary and the way it is related to the admissible domains.

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