Packing Convex Bodies by Cylinders

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 counterp...

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Bibliographic Details
Published in:Discrete & computational geometry 2016-04, Vol.55 (3), p.725-738
Main Authors: Bezdek, Károly, Litvak, Alexander E.
Format: Article
Language:English
Subjects:
Banach spaces
Combinatorics
Computational geometry
Computational Mathematics and Numerical Analysis
Covering
Cylinders
Estimates
Geometry
Lower bounds
Mathematics
Mathematics and Statistics
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Summary: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 ).
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-016-9760-z