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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

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
MathSciNet review: 1246466
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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: http://dx.doi.org/10.1090/S0273-0979-1994-00493-8
PII: S 0273-0979(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