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On the Busemann-Petty problem concerning central sections of centrally symmetric convex bodies


Author: R. J. Gardner
Journal: Bull. Amer. Math. Soc. 30 (1994), 222-226
MSC (2000): Primary 52A38; Secondary 52A40
DOI: https://doi.org/10.1090/S0273-0979-1994-00493-8
MathSciNet review: 1246466
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Abstract | References | Similar Articles | Additional Information

Abstract: We present a method which shows that in $ {\mathbb{E}^3}$ the Busemann-Petty problem, concerning central sections of centrally symmetric convex bodies, has a positive answer. Together with other results, this settles the problem in each dimension.


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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1994-00493-8
Keywords: Busemann-Petty problem, convex body, star body, section, intersection body, spherical Radon transform, Schwarz symmetral, geometric tomography
Article copyright: © Copyright 1994 American Mathematical Society

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