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

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

Abstract. 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)≥ 2cd 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>

István Talata | I. Talata

[1] C. A. Rogers,et al. Packing and Covering , 1964 .

[2] M. Smith. Packing Translates of a Compact Set in Euclidean Space , 1975 .

[3] H. P. F. Swinnerton-Dyer,et al. Extremal lattices of convex bodies , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[4] A. Bezdek,et al. Mutually contiguous translates of a plane disk , 1995 .

[5] E. Straus,et al. On contiguous congruent sets in Euclidean space , 1959 .

[6] C. Shannon. Probability of error for optimal codes in a Gaussian channel , 1959 .

[7] G. Tóth,et al. Packing and Covering with Convex Sets , 1993 .

[8] V. Milman,et al. Asymptotic Theory Of Finite Dimensional Normed Spaces , 1986 .

[9] V. Milman,et al. Almost Euclidean quotient spaces of subspaces of a finite-dimensional normed space , 1985 .

[10] J. Lindenstrauss,et al. The Local Theory of Normed Spaces and its Applications to Convexity , 1993 .

[11] A. Wyner. Capabilities of bounded discrepancy decoding , 1965 .