Intersection bodies and valuations

  title={Intersection bodies and valuations},
  author={Monika Ludwig},
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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Publications referenced by this paper.
Showing 1-10 of 44 references

Intersection bodies and dual mixed volumes

E. Lutwak
Adv. Math. 71 • 1988
View 5 Excerpts
Highly Influenced

Fourier analysis in convex geometry

A. Koldobsky
Mathematical Surveys and Monographs, vol. 116, American Mathematical Society, Providence, RI • 2005
View 1 Excerpt

Minkowski valuations

M. Ludwig
Trans. Amer. Math. Soc. 357 • 2005
View 2 Excerpts

Generalizations of the Busemann-Petty problem for sections of convex bodies

B. Rubin, G. Zhang
J. Funct. Anal. 213 • 2004
View 1 Excerpt

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