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arXiv · 2407.17340

On Generalized Kissing Numbers of Convex Bodies

Yiming Li·Chuanming Zong
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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.

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Yiming Li, Chuanming Zong. 2024-07-24. On Generalized Kissing Numbers of Convex Bodies. https://doi.org/10.1007/s10473-025-0106-x

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