From deep holes to free planes
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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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 39 (2002), 533-555
- MSC (2000): Primary 05B40, 11H31, 52C15, 52C17
- DOI: https://doi.org/10.1090/S0273-0979-02-00950-3
- MathSciNet review: 1920280
Dedicated: Dedicated to Eli Goodman and Ricky Pollack