Segments in Ball Packings

Ball packings with high chromatic numbers from strongly regular graphs

Inspired by Bondarenko’s counter-example to Borsuk’s conjecture, we notice some strongly regular graphs that provide examples of ball packings whose chromatic numbers are significantly higher than the dimensions. In particular, from generalized quadrangles we obtain unit ball packings in dimension q3 − q2 + q with chromatic number q3 + 1, where q is a prime power. This improves the previous low...

Maximal ball packings of symplectic-toric manifolds

Let (M, σ, ψ) be a symplectic-toric manifold of dimension at least four. This paper investigates the symplectic ball packing problem in the toral equivariant setting. We show that the set of toric symplectic ball packings of M admits the structure of a convex polytope. Previous work of the first author shows that up to equivalence, only (CP)2 and CP admit density one packings when n = 2 and onl...

1 Combinatorial scalar curvature andrigidity of ball packings

The Optimal Ball and Horoball Packings of the Coxeter Tilings in the Hyperbolic 3-space

In this paper I describe a method – based on the projective interpretation of the hyperbolic geometry – that determines the data and the density of the optimal ball and horoball packings of each well-known Coxeter tiling (Coxeter honeycomb) in the hyperbolic space H.

The Optimal Ball and Horoball Packings to the Coxeter Honeycombs in the Hyperbolic d-space

In a former paper [18] a method is described that determines the data and the density of the optimal ball or horoball packing to each Coxeter tiling in the hyperbolic 3-space. In this work we extend this procedure – based on the projective interpretation of the hyperbolic geometry – to higher dimensional Coxeter honeycombs in H, (d = 4, 5), and determine the metric data of their optimal ball an...