Abstract
We present generalizations of the Busemann-Petty problem for dual volumes of intermediate central sections of symmetric convex bodies. It is proved that the answer is negative when the dimension of the sections is greater than or equal to 4. For two- three-dimensional sections, both negative and positive answers are given depending on the orders of dual volumes involved, and certain cases remain open. For bodies of revolution, a complete solution is obtained in all dimensions.
Original language | English (US) |
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Pages (from-to) | 473-501 |
Number of pages | 29 |
Journal | Journal of Functional Analysis |
Volume | 213 |
Issue number | 2 |
DOIs | |
State | Published - Aug 15 2004 |
Keywords
- Convex bodies
- Dual volumes
- The Busemann-Petty problem
- The spherical Radon transform
ASJC Scopus subject areas
- Analysis