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Intersection bodies and valuations
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 128, Number 6, December 2006
- pp. 1409-1428
- 10.1353/ajm.2006.0046
- Article
- Additional Information
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All GL (n) covariant star-body-valued valuations on convex polytopes are completely classified. It is shown that there is a unique nontrivial such valuation. This valuation turns out to be the so-called "intersection operator"—an operator that played a critical role in the solution of the Busemann-Petty problem.