Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds - Mathematics > Dynamical SystemsReport as inadecuate




Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds - Mathematics > Dynamical Systems - Download this document for free, or read online. Document in PDF available to download.

Abstract: We obtain an asymptotic formula for the number of circles of curvature atmost T in any given bounded Apollonian circle packing. For an integral packing,we obtain the upper bounds for the number of circles with prime curvature aswell as of pairs of circles with prime curvatures, which are sharp up constantmultiples. The main ingredient of our proof is the effective equidistributionof expanding horospheres on geometrically finite hyperbolic 3-manifolds underthe assumption that the critical exponent of its fundamental group exceeds one.



Author: Alex Kontorovich Brown University, Hee Oh Brown University

Source: https://arxiv.org/







Related documents