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Decomposition of convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

Wolfgang Weil
Wolfgang Weil
Affiliation:
Albert-Ludwigs-Universität, Freiburg
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Extract

1. A convex body K in n-dimensional Euclidean space En (nonvoid, compact, and convex subset of En) is uniquely determined, up to translations, by its mixed volumes with other convex bodies. Therefore one might expect that relations between two convex bodies K and L correspond to relations between the mixed volumes of K, L, and other bodies. In this paper we give conditions, formulated in terms of mixed volumes, which are necessary and sufficient for a certain property of decomposability, namely, the property that L is a summand of K, and we solve some related problems.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 21 , Issue 1 , June 1974 , pp. 19 - 25
Copyright
Copyright © University College London 1974

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References

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