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.
Yiming Li
,
Chuanming Zong
. ON GENERALIZED KISSING NUMBERS OF CONVEX BODIES[J]. Acta mathematica scientia, Series B, 2025
, 45(1)
: 72
-95
.
DOI: 10.1007/s10473-025-0106-x
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