41 citations · 274 across the 53 of their papers we have counts for
6 papers · 1 filter
Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond
Hee Oh
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 fl…
Counting visible circles on the sphere and Kleinian groups
Hee Oh, Nimish Shah
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 $…
On the distribution of orbits of geometrically finite hyperbolic groups on the boundary (with appendix by Francois Maucourant)
Seonhee Lim, Hee Oh
We investigate the distribution of orbits of a non-elementary discrete hyperbolic group acting on the n-dimensional hyperbolic space and its geometric boundary. In particular, we s…
The Asymptotic distribution of circles in the orbits of Kleinian groups
Hee Oh, Nimish Shah
Let P be a locally finite circle packing in the plane invariant under a non-elementary Kleinian group Gamma and with finitely many Gamma-orbits. When Gamma is geometrically finite,…
Almost prime Pythagorean triples in thin orbits
Alex Kontorovich, Hee Oh
For the ternary quadratic form Q(x) = x^2 + y^2 - z^2 and a non-zero Pythagorean triple x_0 in Z^3 lying on the cone Q(x) = 0, we consider an orbit O = x_0 Gamma of a finitely gene…
Equidistribution and Counting for orbits of geometrically finite hyperbolic groups
Hee Oh, Nimish Shah
Let G be the identity component of SO(n,1), acting linearly on a finite dimensional real vector space V. Consider a vector w_0 in V such that the stabilizer of w_0 is a symmetric s…