On the Equicontinuity Region of Discrete Subgroups of PU(1,n)

2008/09/09 by José Seade, Seade, José, Angel Cano +1 · 2 citations
Mathematics · #22E40 #32Q45 #37F45 (Primary) #57R30 (Secondary) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #math.DS #msc:22E40 #msc:32Q45 #msc:37F45 #msc:57R30

paper · pdf · doi:10.48550/arxiv.0809.1546

arxiv created 2008/09/09 · openalex publication_date 2008/09/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a discrete subgroup of PU(1,n). Then G acts on \mathbb Pⁿ_\mathbb C preserving the unit ball \mathbb Hⁿ_\mathbb C, where it acts by isometries with respect to the Bergman metric. In this work we determine the equicontinuty region Eq(G) of G in \mathbb Pⁿ_{\mathbb C}: It is the complement of the union of all complex projective hyperplanes in \mathbb Pⁿ_{\mathbb C} which are tangent to ∂ \mathbb Hⁿ_\mathbb C at points in the Chen-Greenberg limit set Λ_CG(G ), a closed G-invariant subset of ∂ \mathbb Hⁿ_\mathbb C, which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous.

Citations

• Semigroups containing proximal linear maps

Cited by

• Classification of Quaternionic Projective Transformations by Equicontinuity Regions
• Kulkarni limit sets for cyclic quaternionic projective groups

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