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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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From deep holes to free planes
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by Chuanming Zong PDF
Bull. Amer. Math. Soc. 39 (2002), 533-555 Request permission


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:
  • 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
  • © Copyright 2002 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 39 (2002), 533-555
  • MSC (2000): Primary 05B40, 11H31, 52C15, 52C17
  • DOI:
  • MathSciNet review: 1920280