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On Maximal
$k$-Sections and Related Common Transversals of Convex Bodies
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 2004
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