The Lower Dimensional Busemann-Petty Problem for Bodies with the Generalized Axial Symmetry

Details The Lower Dimensional Busemann-Petty Problem for Bodies with the Generalized Axial Symmetry The Lower Dimensional Busemann-Petty Problem for Bodies with the Generalized Axial Symmetry

2007-01-11

arxiv.org/abs/math/0701317v2

Mathematics

Functional Analysis

18 pages

Scientific paper

The lower dimensional Busemann-Petty problem asks, whether n-dimensional centrally symmetric convex bodies with smaller i-dimensional central sections necessarily have smaller volumes. The paper contains a complete solution to the problem when the body with smaller sections is invariant under rotations, preserving mutually orthogonal coordinate subspaces of fixed dimension. The argument relies on the notion of canonical angles between subspaces, spherical Radon transforms, properties of intersection bodies, and the generalized cosine transforms.

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