Original scientific paper

On G-pseudo-centres of convex bodies

Maria Moszynska
Tomasz Zukowski

Abstract

As it is well known, for every convex body A in Rn there is a unique centrally symmetric kernel, that is, a centrally symmetric convex body C ⊂ 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 σ0 every A has a unique G-kernel. If A is strictly convex, then its G-kernel is unique for every G.

Keywords

Convex body; G-invariant convex bod; , n-volume; G-kernel; G-pseudo-centre

Hrčak ID:

8190

URI

https://hrcak.srce.hr/8190

Publication date:

1.12.1998.

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