This is an announcement for the paper "The lower dimensional Busemann-Petty problem for bodies with the generalized axial symmetry" by Boris Rubin.
Abstract: The lower dimensional Busemann-Petty problem asks, whether $n$-dimensional origin-symmetric convex bodies, having smaller $i$-dimensional sections, necessarily have smaller volumes. For $i=1$, the affirmative answer is obvious. For $i>3$, the answer is negative. For $i=2$ and $i=3$, the problem is still open, except when the body with smaller sections is a body of revolution. In this case the answer is affirmative. The paper contains a complete solution to the problem in the more general situation, when the body with smaller sections is invariant under orthogonal transformations preserving coordinate subspaces $R^{l}$ and $R^{n-l}$ of $R^{n}$ for arbitrary fixed $0<l<n$.
Archive classification: Functional Analysis
Mathematics Subject Classification: 44A12; 52A38
Remarks: 26 pages
The source file(s), simplex2.tex: 72011 bytes, is(are) stored in gzipped form as 0701317.gz with size 23kb. The corresponding postcript file has gzipped size 155kb.
Submitted from: borisr@math.lsu.edu
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