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The translative kissing number H(K)  of a d -dimensional convex body K  is the maximum number of mutually nonoverlapping translates of K  which touch K . In this paper we show that there exists an absolute constant c > 0  such that H(K)≥ 2 cd   for every positive integer d  and every d -dimensional convex body K . We also prove a generalization of this result for pairs of centrally symmetric convex bodies.<lsiheader><onlinepub>26 June, 1998<editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt;<pdfname>19n3p447.pdf<pdfexist>yes<htmlexist>no<htmlfexist>no<texexist>yes<sectionname></lsiheader>

Exponential Lower Bound for the Translative Kissing Numbers of d -Dimensional Convex Bodies