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On Maximal
$k$ -Sections and Related Common Transversals of Convex Bodies
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- Journal:
- Canadian Mathematical Bulletin / Volume 47 / Issue 2 / 01 June 2004
- Published online by Cambridge University Press:
- 20 November 2018, pp. 246-256
- Print publication:
- 01 June 2004
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- Article
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Generalizing results from
$[\text{MM}1]$ referring to the intersection body 
$\text{IK}$ and the cross-section body 
$CK$ of a convex body 
$K\,\,\subset \,\,{{\mathbb{R}}^{d}}$ , 
$d\,\ge \,2$ , we prove theorems about maximal $k$ -sections of convex bodies, 
$k\,\in \,\{1,\,\ldots ,\,d\,-\,1\}$ , and, simultaneously, statements about common maximal 
$(d\,-\,1)-$ and 1-transversals of families of convex bodies.
