Counting visible circles on the sphere and Kleinian groups

2010/04/23 by Hee Oh, Nimish Shah, Nimish A. Shah
Mathematics · #Analytic Number Theory Research #Computer science #Content (measure theory) #Mathematical analysis #Mathematics #Mathematics and Applications #Point processes and geometric inequalities #math.DS #math.GT

paper · pdf · doi:10.1017/cbo9781316275849.009

published as In: Geometry, topology, and dynamics in negative curvature, pg. 272--288, London Math. Soc. Lecture Note Series, 425, Cambridge Univ. Press, Cambridge, 2016 · Main results are significantly improved, 16 pages, 1 figure

arxiv created 2010/04/23 · openalex publication_date 2016/01/05 · arxiv updated 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Abstract. For a circle packing P on the sphere invariant under a ge-ometrically finite Kleinian group, we compute the asymptotic of the number of circles in P of spherical curvature at most T which are con-tained in any given region. 1.

Citations

• The density at infinity of a discrete group of hyperbolic motions
• Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond