Bulletin of the American Mathematical Society

Author(s): Chuanming Zong
Journal: Bull. Amer. Math. Soc. 39 (2002), 533-555.
MSC (2000): Primary 05B40, 11H31, 52C15, 52C17
Posted: July 8, 2002
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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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Retrieve articles in Bulletin of the American Mathematical Society with MSC (2000): 05B40, 11H31, 52C15, 52C17

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

DOI: 10.1090/S0273-0979-02-00950-3
PII: S 0273-0979(02)00950-3
Received by editor(s): May 31, 2001,
Received by editor(s) in revised form: January 1, 2002
Posted: July 8, 2002
Dedicated: Dedicated to Eli Goodman and Ricky Pollack
Additional Notes: This work is supported by the National Science Foundation of China and a special grant from Peking University
Copyright of article: Copyright 2002, American Mathematical Society

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