TY - JOUR
T1 - Generalizations of the Busemann-Petty problem for sections of convex bodies
AU - Rubin, Boris
AU - Zhang, Gaoyong
N1 - Funding Information:
·Corresponding author. E-mail addresses: [email protected] (B. Rubin), [email protected] (G. Zhang). 1Supported in part by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany). 2Supported in part by NSF Grant DMS-0104363.
PY - 2004/8/15
Y1 - 2004/8/15
N2 - 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.
AB - 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.
KW - Convex bodies
KW - Dual volumes
KW - The Busemann-Petty problem
KW - The spherical Radon transform
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U2 - 10.1016/j.jfa.2003.10.008
DO - 10.1016/j.jfa.2003.10.008
M3 - Article
AN - SCOPUS:3242883295
SN - 0022-1236
VL - 213
SP - 473
EP - 501
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 2
ER -