Mixed volumes and measures of asymmetry (Q477883)

The paper under review is devoted to the study of relationships between mixed volumes and special measures of asymmetry for convex bodies. One of the main results of the paper (Theorem 3.2) establishes a close connection between the \(L_p\)-mixed volumes proposed by \textit{E. Lutwak} [J. Differ. Geom. 38, No. 1, 131--150 (1993; Zbl 0788.52007)] and the \(p\)-measures of asymmetry, which have the Minkowski measure as a special case, introduced by \textit{Q. Guo} [Adv. Geom. 12, No. 2, 287--301 (2012; Zbl 1242.52004)]. The authors study also a special extension of the \(p\)-measures of asymmetry, that is defined in terms of the Orlicz mixed volumes introduced by R. J. Gardner, D. Hug and W. Weil [\textit{R. J. Gardner} et al., J. Differ. Geom. 97, No. 3, 427--476 (2014; Zbl 1303.52002)].