Kleinian groups are discrete isometry subgroups of the 2- or 3-dimensional hyperbolic spaces. In this talk, we will investigate the Hausdorff dimension of the limit set which consists of the accumulation points of one orbit of the group action. The argument heavily involves the topology and geometry of hyperbolic 2- or 3-manifolds.
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5312