1 research outputs found
Local-global principles in circle packings
We generalize work of Bourgain-Kontorovich and Zhang, proving an almost
local-to-global property for the curvatures of certain circle packings, to a
large class of Kleinian groups. Specifically, we associate in a natural way an
infinite family of integral packings of circles to any Kleinian group satisfying certain conditions, where is an
imaginary quadratic field, and show that the curvatures of the circles in any
such packing satisfy an almost local-to-global principle. A key ingredient in
the proof of this is that possesses a spectral gap property, which
we prove for any infinite-covolume, geometrically finite, Zariski dense
Kleinian group in containing a Zariski dense
subgroup of .Comment: 54 pages, 2 figure