Mathematika

Research Article

Maximal hyperplane sections of convex bodies

Mathieu Meyera1

a1 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.

Abstract

It is shown that the cross-section body of a convex body K 3, 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 3.

(Received January 30 1998)

Key Words:

  • 52A40: CONVEX AND DISCRETE GEOMETRY; General Convexity; Inqualities and extremum problems