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

Published online by Cambridge University Press:  20 November 2018

Endre Makai Jr.  and
Horst Martini
Endre Makai Jr.
Affiliation:
E. Makai, Jr. Alfréd Rényi Mathematical Institute Hungarian Academy of Sciences Pf. 127 H-1364 Budapest Hungary, Email: [email protected]
Horst Martini
Affiliation:
H. Martini University of Technology Chemnitz Faculty of Mathematics D-09107 Chemnitz Germany, Email: [email protected]
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Abstract

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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.

Keywords

52A2055Mxx
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 246 - 256
Copyright
Copyright © Canadian Mathematical Society 2004

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