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Information Center for Mathematical Science

논문검색

Information Center for Mathematical Science

논문검색

Glasnik Matematicki Serja III.
( Vol. 33 NO.2 / (1998))
On G- Pseudo- Centres of Convex Bodies
Maria Moszynska, Tomasz Zukowski,
Pages. 251-265
Abstract As is well known, for every convex body $A$ in $R^n$ there is a unique centrally symmetric kernel, that is, a centrally symmetric convex body $Csubset A$ with maximal $n$-volume. The paper concerns $G$-kernels of a convex body $A$ for any subgroup $G$ of $O(n)$, i.e. $G$-invariant convex subsets of $A$ with maximal
$n$-volume. We prove that only for $G$ generated by the central symmetry
$sigma_0$ every $A$ has a unique $G$-kernel. If $A$ is strictly convex, then
its $G$-kernel is unique for every $G$.
Contents Introduction
1. Preliminaries
2. Invariant convex bodies
3. $G$-pseudo and $G$-kernels of a convex body
4. The uniqueness of $G$-kernel for an affine image
Key words convex body, $G$-invariant convex body, $n$-volume, $G$-kernel, $G$-pseudo-centre
Mathmatical Subject Classification 52A20, 52A38, 52A99