Coverings by Planks and Cylinders

  • Károly Bezdek
Part of the CMS Books in Mathematics book series (CMSBM)


As usual, a convex body of the Euclidean space \(\mathbb{E}^d\) is a compact convex set with non-empty interior. Let C\(\mathbb{E}^d\) be a convex body, and let H\(\mathbb{E}^d\) be a hyperplane. Then the distance w(C;H) between the two supporting hyperplanes of C parallel to H is called the width of C parallel to H. Moreover, the smallest width of C parallel to hyperplanes of \(\mathbb{E}^d\) is called the minimal width of C and is denoted by w(C).


Convex Body Real Hilbert Space Integer Point Minimal Width Symmetric Convex Body 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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