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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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3. Ball, K. M.. Cube slicing in Rn. Proc. Amer. Math. Soc., 97 (1986), 465–473.Google Scholar
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