Metric conformal structures and hyperbolic dimension

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)137-163
Number of pages27
JournalConformal Geometry and Dynamics
Issue number11
StatePublished - Sep 12 2007

ASJC Scopus subject areas

  • Geometry and Topology


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