Linear programming bounds in homogeneous spaces, I: Optimal packing density
Maximilian Wackenhuth
TL;DR
This paper develops linear programming bounds for sphere packing densities in homogeneous spaces, successfully addressing a conjecture for hyperbolic space and providing optimal bounds for packing problems.
Contribution
It introduces linear programming bounds for packing densities in homogeneous spaces and proves a conjecture for hyperbolic space.
Findings
Established linear programming bounds for sphere packings in homogeneous spaces
Solved a conjecture by Cohn and Zhao for hyperbolic space
Provided optimal packing density bounds
Abstract
In this article we obtain linear programming bounds for the maximal sphere packing density of commutative spaces. A special case of our results solves a conjecture by Cohn and Zhao on linear programming bounds for sphere packings in hyperbolic space.
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Taxonomy
TopicsPoint processes and geometric inequalities · Geometric Analysis and Curvature Flows · Geometric and Algebraic Topology