\(k\)-codimensional projection bodies
Motivated by the definition of the well-known projection body (see [\textit{C. M. Petty}, Proc. Colloq. Convexity, Copenhagen 1965, 234--241 (1967; Zbl 0152.20601); \textit{T. Wang}, Adv. Math. 230, No. 4--6, 2457--2473 (2012; Zbl 1257.46016)]), the authors introduce \(k\)-codimensional projection bodies for sets of finite permiter. This is a convex body in \(\mathbb{R}^{n-k+1}\), and it depends on the choice of the coordinate system. The case \(k=1\) corresponds to the classical \(n\)-dimensional projection body only for special sets. In analogy to the classical setting, the authors prove \(k\)-codimensional projection inequalities.
scientific article; zbMATH DE number 7595591
scientific article