For any hyperbolic complex X and a ∈ X we construct a visual metric d = da on ∂X that makes the Isom(X)-action on ∂X bi-Lipschitz, Möbius, symmetric and conformal. We define a stereographic projection of da and show that it is a metric conformally equivalent to da. We also introduce a notion of hyperbolic dimension for hyperbolic spaces with group actions. Problems related to hyperbolic dimension are discussed.
|Original language||English (US)|
|Number of pages||27|
|Journal||Conformal Geometry and Dynamics|
|State||Published - Sep 12 2007|
ASJC Scopus subject areas
- Geometry and Topology