Effective circle count for Apollonian packings and closed horospheres

DOI10.1007/s00039-013-0217-8zbMath1276.52019arXiv1202.1067OpenAlexW2963649987MaRDI QIDQ2375771

Hee Oh, Min Lee

Publication date: 25 June 2013

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.1067

zbMATH Keywords

equidistributionhyperbolic 3-manifoldhorosphereApollonian circle packing\(L^2\) spectral gap

Mathematics Subject Classification ID

Circle packings and discrete conformal geometry (52C26)

Related Items (11)

On the rate of equidistribution of expanding horospheres in finite-volume quotients of \(\mathrm{SL}(2,\mathbb{C})\) ⋮ Effective equidistribution of circles in the limit sets of Kleinian groups ⋮ Counting problems for special-orthogonal Anosov representations ⋮ Apollonian packings and Kac-Moody root systems ⋮ Counting common perpendicular arcs in negative curvature ⋮ From Apollonius to Zaremba: Local-global phenomena in thin orbits ⋮ Counting problems in Apollonian packings ⋮ Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of $\operatorname {SL}_2(\mathbb {Z})$ ⋮ Apollonian circle packings: dynamics and number theory ⋮ On the rate of equidistribution of expanding translates of horospheres in \(\Gamma\backslash G\) ⋮ Asymptotic Counting in Conformal Dynamical Systems

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