Modified Busemann-Petty problem on sections of convex bodies |
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Authors: | A Koldobsky V Yaskin M Yaskina |
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Institution: | (1) Department of Mathematics, University of Missouri, 65211 Columbia, MO, USA |
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Abstract: | The Busemann-Petty problem asks whether convex origin-symmetric bodies in ℝ
n
with smaller central hyperplane sections necessarily have smallern-dimensional volume. It is known that the answer is affirmative ifn≤4 and negative ifn≥5. In this article we replace the assumptions of the original Busemann-Petty problem by certain conditions on the volumes
of central hyperplane sections so that the answer becomes affirmative in all dimensions.
The first-named author was supported in part by the NSF grant DMS-0136022 and by a grant from the University of Missouri Research
Board. |
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Keywords: | |
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