On Generalized Kissing Numbers of Convex Bodies
Metric Geometry
2025-09-16 v1
Abstract
In 1694, Gregory and Newton proposed the problem to determine the kissing number of a rigid material ball. This problem and its higher dimensional generalization have been studied by many mathematicians, including Minkowski, van der Waerden, Hadwiger, Swinnerton-Dyer, Watson, Levenshtein, Odlyzko, Sloane and Musin. In this paper, we introduce and study a further generalization of the kissing numbers for convex bodies and obtain some exact results, in particular for balls in dimensions three, four and eight.
Keywords
Cite
@article{arxiv.2407.17340,
title = {On Generalized Kissing Numbers of Convex Bodies},
author = {Yiming Li and Chuanming Zong},
journal= {arXiv preprint arXiv:2407.17340},
year = {2025}
}
Comments
26 pages, 3 figures