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Minkowski valuations
Centroid and difference bodies define $\operatorname {SL}(n)$ equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of $\operatorname {SL}(n)$ equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of $\operatorname {SL}(n)$ contravariant Minkowski valuations …