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From deep holes to free planes


Author: Chuanming Zong
Journal: Bull. Amer. Math. Soc. 39 (2002), 533-555
MSC (2000): Primary 05B40, 11H31, 52C15, 52C17
Published electronically: July 8, 2002
MathSciNet review: 1920280
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Abstract | References | Similar Articles | Additional Information

Abstract: During the last decades, by applying techniques from Number Theory, Combinatorics and Measure Theory, remarkable progress has been made in the study of deep holes, free planes and related topics in packings of convex bodies, especially in lattice ball packings. Meanwhile, some fascinating new problems have been proposed. To stimulate further research in related areas, we will review the main results, some key techniques and some fundamental problems about deep holes, free cylinders and free planes in this paper.


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Additional Information

Chuanming Zong
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China
Email: cmzong@math.pku.edu.cn

DOI: http://dx.doi.org/10.1090/S0273-0979-02-00950-3
Received by editor(s): May 31, 2001
Received by editor(s) in revised form: January 1, 2002
Published electronically: July 8, 2002
Additional Notes: This work is supported by the National Science Foundation of China and a special grant from Peking University
Dedicated: Dedicated to Eli Goodman and Ricky Pollack
Article copyright: © Copyright 2002 American Mathematical Society