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Maximal sections and centrally symmetric bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

E. Makai Jr ,
H. Martini  and
T. Ódor
E. Makai Jr
Affiliation:
Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, Hungary. E-mail: makai@renyi.hu
H. Martini
Affiliation:
Techńische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany. E-mail: martini@mathematik.tu-chemnitz.de
T. Ódor
Affiliation:
Alfréd Rényi Mathematical Institute, Hungarian Academy of Sciences, P.O.B. 127, H-1364 Budapest, Hungary. E-mail: odor@math.u-szeged.hu
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Abstract

Let d≥2 and let K⊂ℝd be a convex body containing the origin 0 in its interior. For each direction ω, let the (d−l)-volume of the intersection of K and an arbitrary hyperplane with normal ω attain its maximum when the hyperplane contains 0. Then K is symmetric about 0. The proof uses a linear integro-differential operator on Sd−1, whose null-space needs to be, and will be determined.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 19 - 30
Copyright
Copyright © University College London 2000

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