The limit set of discrete subgroups of PSL(3,\C)

2010/01/29 by Waldemar Barrera, Barrera, Waldemar, Angel Cano +3
Mathematics · #32Q45 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #math.CV #math.DG #msc:32Q45

paper · pdf · doi:10.48550/arxiv.1002.0021

arxiv created 2010/01/29 · arxiv updated 2010/02/26

Abstract

If Γ is a discrete subgroup of PSL(3,ℂ), it is determined the equicontinuity region Eq(Γ) of the natural action of Γ on ℙ²_ℂ. It is also proved that the action restricted to Eq(Γ) is discontinuous, and Eq(Γ) agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of Γ in the sense of Kulkarni, Λ(Γ), contains at least three lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which Γ acts discontinuously. Moreover, if Λ(Γ) contains at least four complex lines and Γ acts on ℙ²_ℂ without fixed points nor invariant lines, then each connected component of Eq(Γ) is a holomorphy domain and a complete Kobayashi hyperbolic space.

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