A note on the Busemann-Petty problem for bodies of certain invariance

Details A note on the Busemann-Petty problem for bodies of certain invariance A note on the Busemann-Petty problem for bodies of certain invariance

2008-11-10

arxiv.org/abs/0811.1593v2

Mathematics

Functional Analysis

Scientific paper

The Busemann-Petty problem asks whether origin symmetric convex bodies in $\R^n$ with smaller hyperplane sections necessarily have smaller volume. The answer is affirmative if $n\leq 3$ and negative if $n\geq 4.$ We consider a class of convex bodies that have a certain invariance property with respect to their ordered k-tuples of coordinates in $\R^{kn}$ and prove the corresponding problem.

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