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Centrally symmetric convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Paul R. Goodey
Paul R. Goodey
Affiliation:
Mathematics Department, University of Oklahoma, Norman, OK 73019, U.S.A.
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Abstract

The principal objective of this work is to investigate various classes of centrally symmetric convex sets. These classes range from the zonoids at one extreme to the class of all centrally symmetric bodies at the other. The defining properties of these classes involve inequalities between mixed volumes. Various other characterizations will be found in response to a number of questions in a recent survey article by Rolf Schneider and Wolfgang Weil. Some of these are concerned with measures on a Grassmannian manifold while others relate to the intermediate surface area measures of convex bodies. We shall also show these classes are characterized by certain extremal geometric inequalities. The work concludes with a brief discussion of related results concerned with generalized zonoids.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 31 , Issue 2 , December 1984 , pp. 305 - 322
Copyright
Copyright © University College London 1984

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