Generalizations of the Busemann-Petty problem for sections of convex bodies |
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Authors: | Boris Rubin Gaoyong Zhang |
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Institution: | a Institute of Mathematics, Hebrew University, Jerusalem 91904, Israel b Department of Mathematics, Polytechnic University, 6 Metrotech Center, Brooklyn, NY 11201, USA |
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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. |
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Keywords: | primary 52A38 secondary 44A12 |
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