Bounds for several-disk packings of hyperbolic surfaces

Abstract

For any given natural number $k$, this paper gives upper bounds on the radius of a packing of a complete hyperbolic surface of finite area by $k$ equal-radius disks in terms of the surface's topology. We show that the bounds given here are sharp in some cases and not sharp in others.

arXiv commentRevised following referee's comments. Minor corrections and changes to exposition