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Maximal hyperplane sections of convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Mathieu Meyer
Mathieu Meyer
Affiliation:
Equipe d'Analyse et de Mathematiques Appliquees, Université de Marne-la-Valleé, Cité Descartes, 5, boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Valée, Cedex 2, France.
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Abstract

It is shown that the cross-section body of a convex body K ⊂ ℝ3, that is the symmetric body which has for radial function in the direction u the maximal volume of a section of K by an hyperplane orthogonal to u, is a convex body in ℝ3.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 46 , Issue 1 , June 1999 , pp. 131 - 136
Copyright
Copyright © University College London 1999

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References

Br.Brehm, U.. Convex polytopes with non-convex cross-section bodies. Mathematika (this volume), 127–129.Google Scholar
Bu.Busemann, H.. A theorem on convex bodies of the Brunn-Minkowski type. Proc. Nat. Acad. U.S.A. 35, (1949), 27–31.Google Scholar
3.Fradelizi, F. M.. Hyperplane sections of convex bodies in isotropic position. Contributions to Algebra and Geometry, 40 (1999), 163–183.Google Scholar
G.Gardner, R. J.. Geometric Tomography (Cambridge University Press, 1995).Google Scholar
MM1.JrMakai, E. and Martini, H.. The Cross-Section Body, Plane Sections of Convex Bodies and Approximation of Convex Bodies, I. Geometriae Dedicata, 63, (1996), 267–296.CrossRefGoogle Scholar
MM2.JrMakai, E. and Martini, H.. The Cross-Section Body, Plane Sections of Convex Bodies and Approximation of Convex Bodies, II. Geometriae Dedicata, 70 (1998), 283–303.CrossRefGoogle Scholar
M1.Martini, H.. Extremal equalities for cross-sectional measures of convex bodies. Proc. 3rd Geometry Congress, Aristoteles Univ. Thessaloniki. (Aristoteles University Press, 1992), 285–296.Google Scholar
M2.Martini, H.. Cross-sectional measures. Colloquia Matematica Societatis Jànos Bolyai, 63, Intuitive Geometry (Szeged 1991). Ed. by Böröcsky, K. and Tóth, G. Fejes. (North Holland, 1994) 269–310.Google Scholar