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A note on a problem of H. Busemann and C. M. Petty concerning sections of symmetric convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Apostolos A. Giannopoulos
Apostolos A. Giannopoulos
Affiliation:
Mathematics Department, University of Crete, Iraklion, Crete, Greece.
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Abstract

Let

It is proved that for suitable a and b, n≥7, one can have Vn(An) = Vn(Bn) and for every (n–1)-dimensional subspace H of ℝn, where Bn is the unit ball of ℝn. This strengthens previous negative results on a problem of H. Busemann and C. M. Petty.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 239 - 244
Copyright
Copyright © University College London 1990

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References

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4. Ball, K. M.. Some remarks on the geometry of convex sets. Geometric aspects of Functional Analysis, Springer Lecture Notes 1317 (1988), 224–231.CrossRefGoogle Scholar