# The limit set of discrete subgroups of $PSL3,C$ - Mathematics > Differential Geometry

The limit set of discrete subgroups of $PSL3,C$ - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: If $\Gamma$ is a discrete subgroup of $PSL3,\Bbb{C}$, it is determined theequicontinuity region $Eq\Gamma$ of the natural action of $\Gamma$ on$\Bbb{P}^2 \Bbb{C}$. It is also proved that the action restricted to$Eq\Gamma$ is discontinuous, and $Eq\Gamma$ agrees with the discontinuityset in the sense of Kulkarni whenever the limit set of $\Gamma$ in the sense ofKulkarni, $\Lambda\Gamma$, contains at least three lines in general position.Under some additional hypothesis, it turns out to be the largest open set onwhich $\Gamma$ acts discontinuously. Moreover, if $\Lambda\Gamma$ contains atleast four complex lines and $\Gamma$ acts on $\Bbb{P}^2 \Bbb{C}$ without fixedpoints nor invariant lines, then each connected component of $Eq\Gamma$ is aholomorphy domain and a complete Kobayashi hyperbolic space.

Author: ** Waldemar Barrera, Angel Cano, Juan Pablo Navarrete**

Source: https://arxiv.org/