On symmetric versions of Sylvester's problem

Details On symmetric versions of Sylvester's problem On symmetric versions of Sylvester's problem

2003-05-28

arxiv.org/abs/math/0305411v1

Monatsh. Math. 145 no. 4, 307-319 (2005)

Mathematics

Metric Geometry

AMS-LaTeX

Scientific paper

10.1007/s00605-005-0300-9

We consider moments of the normalized volume of a symmetric or nonsymmetric
random polytope in a fixed symmetric convex body. We investigate for which
bodies these moments are extremized, and calculate exact values in some of the
extreme cases. We show that these moments are maximized among planar convex
bodies by parallelograms.

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