Intersection bodies and valuations

@inproceedings{Ludwig2005IntersectionBA,
  title={Intersection bodies and valuations},
  author={Monika Ludwig},
  year={2005}
}
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) A function Z defined on the set K of convex bodies (that is, of convex compact sets) in Rn or on a certain subset C of K and… CONTINUE READING
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