Kissing number in spherical space
Maria Dostert, Alexander Kolpakov

TL;DR
This paper explores how the maximum number of non-overlapping equal spheres that can touch a central sphere in spherical space varies with radius, providing high-accuracy bounds using advanced optimization and coding techniques.
Contribution
It introduces new upper and lower bounds for the kissing number in spherical space that depend on the sphere radius, improving understanding of this geometric problem.
Findings
Graph of kissing number versus radius with high accuracy
New bounds derived via semidefinite programming and spherical codes
Enhanced understanding of sphere packings in spherical geometry
Abstract
This paper investigates the behaviour of the kissing number of congruent radius spheres in , for . Such a quantity depends on the radius , and we plot the approximate graph of with relatively high accuracy by using new upper and lower bounds that are produced via semidefinite programming and by using spherical codes, respectively.
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Taxonomy
TopicsMathematical Approximation and Integration · Computational Geometry and Mesh Generation · Markov Chains and Monte Carlo Methods
