# Bounds for several-disk packings of hyperbolic surfaces

## TL;DR

This paper establishes upper bounds on the radius of packings of hyperbolic surfaces by equal disks, relating these bounds to the surface's topology, and discusses their sharpness in various cases.

## Contribution

It provides new topologically dependent bounds for disk packings on hyperbolic surfaces, including cases where these bounds are sharp.

## Key findings

- Bounds are sharp in some cases.
- Bounds depend on the surface's topology.
- Not all bounds are sharp in every case.

## 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.