\(L_p\)-dual affine surface area
A definition of affine surface area \(\Omega(K)\) of a convex body \(K\) in \(\mathbb{R}^n\) by \textit{K. Leichtweiß} [Manuscr. Math. 65, No.~2, 181--197 (1989; Zbl 0685.53012)] was generalized by \textit{E. Lutwak} [Adv. Math. 118, No.~2, 244--294 (1996; Zbl 0853.52005)] to \(L_p\)-affine surface area \(\Omega_p(K)\) by using Brunn-Minkowski-Fiery theory. In the present paper, the authors introduce \(L_p\)-dual affine surface area using \(L_p\)-dual mixed volumes defined by E. Lutwak [loc. cit.]. With respect to this area functional inequalities are presented (affine isoperimetric, Blaschke-Santaló, Brunn-Minkowski).
scientific article; zbMATH DE number 5355971
scientific article