Density bounds for outer parallel domains of unit ball packings
Karoly Bezdek, Zsolt Langi
TL;DR
This paper establishes upper bounds on the density of unit ball packings relative to their outer parallel domains, explores their relation to contact numbers, and introduces packings of soft balls with bounds on space coverage.
Contribution
It provides new density bounds for outer parallel domains of ball packings and extends the concept to soft ball packings with coverage limits.
Findings
Upper bounds for density relative to outer parallel domains
Connection between density bounds and contact numbers
Bounds on space coverage for soft ball packings
Abstract
We give upper bounds for the density of unit ball packings relative to their outer parallel domains and discuss their connection to contact numbers. Also, packings of soft balls are introduced and upper bounds are given for the fraction of space covered by them.
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