Counting visible circles on the sphere and Kleinian groups

Abstract

For a circle packing P on the sphere invariant under a geometrically finite Kleinian group, we compute the asymptotic of the number of circles in P of spherical curvature at most $T$ which are contained in any given region.

Main results are significantly improved, 16 pages, 1 figure

References in corpus (3)

• Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
• The Asymptotic distribution of circles in the orbits of Kleinian groups
• Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond

Cited by in corpus (5)

• Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
• Counting common perpendicular arcs in negative curvature
• Harmonic analysis, Ergodic theory and Counting for thin groups
• Circle packings, kissing reflection groups and critically fixed anti-rational maps
• Effective bisector estimate with application to Apollonian circle packings