2011/05/22 by Szirmai, Jenő
Mathematics · #52B15 #52C17 #52C22 #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Point processes and geometric inequalities #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1105.4315
openalex publication_date 2011/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper to determine the locally densest horoball packing arrangements and their densities with respect to fully asymptotic tetrahedra with at least one plane of symmetry in hyperbolic 3-space H3 extended with its absolute figure, where the ideal centers of horoballs give rise to vertices of a fully asymptotic tetrahedron. We allow horoballs of different types at the various vertices. Moreover, we generalize the notion of the simplicial density function in the extended hyperbolic space Hn, ~(n ≥ 2), and prove that, in this sense, \it the well known Böröczky--Florian density upper bound for "congruent horoball" packings of H3 does not remain valid to the fully asymptotic tetrahedra. The density of this locally densest packing is ≈ 0.874994, may be surprisingly larger than the Böröczky--Florian density upper bound ≈ 0.853276 but our local ball arrangement seems not to have extension to the whole hyperbolic space.