Glasnik Matematicki, Vol. 33, No.2 (1998), 251-265.
ON G-PSEUDO-CENTRES OF CONVEX BODIES
Maria Moszynska and Tomasz Zukowski
Institute of Matematics, Warsaw University, ul. Banacha 2,
02-097 Warszawa, Poland
Abstract. As it is well known, for every convex body
there is a unique centrally symmetric kernel, that is, a centrally
symmetric convex body C
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
every A has a unique G-kernel. If A is strictly
convex, then its G-kernel is unique for every G.
1991 Mathematics Subject Classification.
52A20, 52A38, 52A99.
Key words and phrases. Convex body, G-invariant
convex body, n-volume, G-kernel,
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