Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond
arXiv:1006.2590
Abstract
We present recent results on counting and distribution of circles in a given circle packing invariant under a geometrically finite Kleinian group and discuss how the dynamics of flows on geometrically finite hyperbolic manifolds are related. Our results apply to Apollonian circle packings, Sierpinski curves, Schottky dances, etc.
To appear in the Proceedings of ICM, 2010