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Modified Busemann-Petty problem on sections of convex bodies

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Abstract

The Busemann-Petty problem asks whether convex origin-symmetric bodies in ℝn 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Missouri, 65211, Columbia, MO, USA

    A. Koldobsky, V. Yaskin & M. Yaskina

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  1. A. Koldobsky
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  2. V. Yaskin
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  3. M. Yaskina
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Additional information

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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Koldobsky, A., Yaskin, V. & Yaskina, M. Modified Busemann-Petty problem on sections of convex bodies. Isr. J. Math. 154, 191–207 (2006). https://doi.org/10.1007/BF02773605

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  • DOI: https://doi.org/10.1007/BF02773605

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