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The volume of certain convex sets

Published online by Cambridge University Press:  24 October 2008

P. McMullen
P. McMullen
Affiliation:
University College, London
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Abstract

Let Ll …, Lr be independent linear subspaces of Ed, with di = dim Li ≥ 1 (i = 1, …, r), and Ed = L1 + … + Lr. For each i, let K¯;i be a convex body in Li with 0 ∈ K¯i, Ki = K¯i + ti(ti ∈ Ed) any translate of K¯i, and define K = con v (K1 ∪ … ∪ Kr), and similarl K¯. Then vol K ≥ vol K¯. Necessary and sufficient conditions for equality are also obtained.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 91 , Issue 1 , January 1982 , pp. 91 - 97
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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