Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T12:04:07.590Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bolker, E. D.. “A class of convex bodies”, Trans. Amer. Math. Soc, 145 (1969), 323–345.CrossRefGoogle Scholar
2.Kelly, J. B.. “Hypermetric spaces” in: The geometry of metric and linear spaces, Lecture Notes in i Mathematics, 490 (Springer-Verlag, 1975), 17–31.Google Scholar
3.Mitrinović, D. S.. Analytic inequalities (Springer-Verlag, 1970).CrossRefGoogle Scholar
4.Schneider, R.. “Über eine Integralgleichung in der Theorie der konvexen Körper“, Math. Nachr., 44 (1970), 55–75.Google Scholar
5.Smiley, D. M. and Smiley, M. F.. “The polygonal inequalities”, Amer. Math. Monthly, 71 (1964), 755–760.Google Scholar
6.Witsenhausen, H. S.. “Metric inequalities and the zonoid problem”, Proc. Amer. Math. Soc, 40 (1973), 517–520.CrossRefGoogle Scholar