On Maximal $k$ -Sections and Related Common Transversals of Convex Bodies

Jr., Endre Makai ; Martini, Horst

Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 246-256

Résumé

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.

Détail

DOI : 10.4153/CMB-2004-024-3

Mots-clés : 52A20, 55Mxx

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