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- W3102059931 abstract "A classification of |$mathrm{SL}(n)$| contravariant, continuous function-valued valuations on convex bodies is established. Such valuations are natural extensions of |$mathrm{SL}(n)$| 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 |$p geq 1$|. 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." @default.
- W3102059931 created "2020-11-23" @default.
- W3102059931 creator A5016221844 @default.
- W3102059931 date "2018-10-03" @default.
- W3102059931 modified "2023-09-26" @default.
- W3102059931 title "Affine Function-Valued Valuations" @default.
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- W3102059931 doi "https://doi.org/10.1093/imrn/rny212" @default.
- W3102059931 hasPublicationYear "2018" @default.
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