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A support characterization of zonotopes

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

H. S. Witsenhausen
H. S. Witsenhausen
Affiliation:
Bell Laboratories, Murray Hill, New Jersey, U.S.A.
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Abstract

A convex polytope is a zonotope, if, and only if, its support function satisfies Hlawka's inequality. It follows that a finite dimensional real space with piecewise linear norm is isometrically isomorphic to a subspace of an L1 space, if, and only if, it has the quadrilateral property

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 25 , Issue 1 , June 1978 , pp. 13 - 16
Copyright
Copyright © University College London 1978

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References

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