Intersection bodies and valuations

Monika. Ludwig
2006 American Journal of Mathematics  
All GL(n) covariant star-body-valued valuations on convex polytopes are completely classified. It is shown that there is a unique non-trivial 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. 2000 AMS subject classification: 52A20 (52B11, 52B45)
doi:10.1353/ajm.2006.0046 fatcat:4ekzyequczbznfwz2axsccwozi