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On the union of convex bodies with no interior point in common

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

P. R. Scott
P. R. Scott
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, SA 5001, South Australia.
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Extract

Let K1, K2,…, Kd+1 be d+1 convex bodies in Ed, the interiors of which have no point in common. If mX denotes the measure of set X, we prove

and this inequality is best possible.

MSC classification

Secondary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Type
Research Article
Information
Mathematika , Volume 37 , Issue 2 , December 1990 , pp. 245 - 250
Copyright
Copyright © University College London 1990

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References

1. Eggleston, H. G.. Convexity. Cambridge Tract No. 47 (Cambridge University Press, 1963).Google Scholar
2. Grünbaum, B.. Partitions of mass-distributions and of convex bodies by hyperplanes. Pacific J. Math., 10 (1960), 1257–1261.CrossRefGoogle Scholar
3. Scott, P. R.. On three sets with no point in common. Mathematika, 25 (1978), 17–23.CrossRefGoogle Scholar
4. Yaglom, I. M. and Boltyanskiĭ, V. G.. Convex Figures (Holt, Rinehart and Winston, 1961).Google Scholar