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Packing Convex Bodies by Cylinders

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Abstract

In Bezdek and Litvak (J Geom Anal 19:233–243, 2009) in relation to the unsolved Bang’s plank problem (Proc Am Math Soc 2:990–993, 1951) we obtained a lower bound for the sum of relevant measures of cylinders covering a given d-dimensional convex body. In this paper we provide the packing counterpart of these estimates. We also extend bounds to the case of r-fold covering and packing and show a packing analog of Falconer’s results (Math Proc Camb Philos Soc 87:81–96, 1980).

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Acknowledgments

The authors would like to thank R. Karasev for comments on Remark 3.2 and the anonymous referee for remarks and careful reading. Partially supported by a Natural Sciences and Engineering Research Council of Canada Discovery Grant.

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Correspondence to Alexander E. Litvak.

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Editor in Charge: János Pach

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Bezdek, K., Litvak, A.E. Packing Convex Bodies by Cylinders. Discrete Comput Geom 55, 725–738 (2016). https://doi.org/10.1007/s00454-016-9760-z

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  • DOI: https://doi.org/10.1007/s00454-016-9760-z

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