Affine Function-Valued Valuations. (3rd October 2018) - Li, Jin
Abstract: A classification of SL(n) contravariant, continuous function-valued valuations on convex bodies is established. Such valuations are natural extensions of SL(n) contravariant L_p Minkowski valuations, the classification of which characterized L_p projection bodies, which are fundamental in the L_p Brunn–Minkowski theory, for p ≥ 1 . Hence, our result will help to better understand extensions of the L_p Brunn–Minkowski theory. In fact, our results characterize general projection functions, which extend L_p projection functions (p -th powers of the support functions of L_p projection bodies) to projection functions in the L_p Brunn–Minkowski theory for 0< p < 1 and in the Orlicz Brunn–Minkowski theory.