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A classification of SL$(n)$ contravariant $\mathcal{C}(\mathbb{R}^n)$ valued valuations on convex bodies is established. Such valuations turn out to be the volume, the Euler characteristic (as constant functions) and general projection… Click to show full abstract
A classification of SL$(n)$ contravariant $\mathcal{C}(\mathbb{R}^n)$ valued valuations on convex bodies is established. Such valuations turn out to be the volume, the Euler characteristic (as constant functions) and general projection functions. The classical ($p=1$) and $L_p$ projection functions for $p>1$ are $p$-th powers of the support functions of $L_p$ projection bodies. Those projection functions were characterized before by Haberl, Ludwig, Parapatits, Schuster and Wannerer with additional homogeneity assumptions. Our results also characterize general projection functions including $L_p$ projection functions for $0
Journal Title: International Mathematics Research Notices
Year Published: 2018
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