Minkowski valuations

Monika Ludwig
2004 Transactions of the American Mathematical Society  
Centroid and difference bodies define SL(n) equivariant operators on convex bodies and these operators are valuations with respect to Minkowski addition. We derive a classification of SL(n) equivariant Minkowski valuations and give a characterization of these operators. We also derive a classification of SL(n) contravariant Minkowski valuations and of L p -Minkowski valuations.
doi:10.1090/s0002-9947-04-03666-9 fatcat:xcsayff47ncvjemfvt43qwxl5y