2007/01/11 by Boris Rubin, Rubin, Boris
Mathematics · #44A12 #52A38 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:44A12 #msc:52A38
paper · pdf · doi:10.48550/arxiv.math/0701317
18 pages
arxiv created 2007/05/03 · arxiv updated 2009/12/01
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.